Sure you can create a room that doesn’t fit in a house. But it’s so dissonant that you either spend thousands and thousands remaking the rest of the house (for it to be outdated when you finish) or you redo the room you just redid.

Your house is the boss. Do what it tells you it wants.

Gray has been done with for a couple of years. Warm tones are what are taking over.

If you prefer cool tones that's one thing, but please do not select a cool color scheme based on thinking it's modern. Gray tones are no longer in fashion in current kitchen remodels, and many home improvement shows where they are featured are now in old reruns. Everything is going towards warmer tones right now as far as trends are concerned. Back to your original question though yes you can blend cool and warm colors if you do it correctly. Starting with your floor I would recommend that you look at very light bleached White Oak tones. This is pretty popular right now so you should be able to find this type of color in some brand if you were going with LVP. Now if you were doing tile I might recommend a marble look-alike tile. Then on to the cabinets, yes you can do white, however, if you're really wanting to incorporate some blue this might be the place to do it. It is not just the hue alone like blue that makes a difference but the tint or tone of it, in other words how dark or light it is. Can you give us more direction in terms of the type of blue you like? Are you thinking dark blue or are you thinking pastel blue or are you thinking medium blue? I'm thinking that a really dark blue would give a better chance of blending with warm tones in other areas because then you almost bring it into the dark neutral tone category. Be aware that white cabinetry has had a really long run in the design world and natural wood tones are taking over in terms of the direction for cabinetry. This is a delicate topic because you will get many people who will debate that white will always be classic. However, in terms of trends, wood tones are really active right now for kitchen cabinetry. Color is so subjective. You can take two colors that wouldn't traditionally be thought of as going together and if you can mix and blend and repeat then you can actually make it work. You are ahead of the game compared to most people by already thinking of keeping your cool and warm tones separate because that is a common mistake. People may have cool tones throughout the whole house and then do a bathroom in warm tones, and it just doesn't fit with the overall scheme. Sounds like you have the opposite--you want to put a cool kitchen in a warm home. White is really the ultimate neutral, and if you look for inspiration photos of white next to warm wood tones, you'll actually find a lot of photos where it works. The blue is going to be a little bit harder to incorporate, but if you can give us an idea of what you want maybe we can give further input

You could do a black marble LVT and still have blue accessories along with some wood cutting boards for adding warmth. That would look great against wood look flooring and be low maintenance for rental too. Just get great undercabinet lighting and overhead lighting.

Here are some inspirations. You can do whatever renters might want. It can be totally different if market supports look.

Matching flooring throughout a small apartment will make it appear larger and using the flooring tone will dctate the rest of tone - warm or -cool. Using the wam tone will imbue the “older home historic warmth with modern convenience. You also do not have to use a dark backsplash as pictured in the warm concept. Use a light backsplash and undercabinet lighting. Your renters will appreciate your commitment to the home’s heritage.

Tread carefully here. About 4 years ago, I changed my master bath to "cool" in my otherwise warm home. I'm now seeking estimates to tear it out and start over. Check out Semihandmade for inspiration (e.g., https://www.houzz.com/photos/douglas-fir-ikea-kitchen-contemporary-kitchen-seattle-phvw-vp~9942302). Warm can be modern and gorgeous, with the right design.

I would stay warm.

White can be either warm or cool. My house has a ton of custom walnut trim and is painted Antique White (SW) throughout. My white kitchen is SW creamy. You CAN do a “white warm” kitchen. I would absolutely do white since it’s timeless. The floors should be a light oak LVP as suggested. I rarely disagree with @Flo Mangan, but black floors are tough to keep clean. Rentals should be easy cleaning surfaces so for your countertop consider Silestone or even laminate. You may be able to find remnants of granite which is usually indestructible and will upgrade the look. Avoid hardware styles that have the metal handle going past the post since those are treacherous for little ones and clothing. You can add the complementary shade of blue in accessories, a curtain or other decorative items.

I could see a combo of timeless style cabinets, and woods with some more modern features. Lots of ways to go.

Or paint the island a warm blue.

Did I miss where the OP said this was a rental?

Thanks to everyone who's taken the time to respond.

@Aglitter, it is indeed a rental. I didn't mention it but I think people inferred it based on my mention of it being an upstairs apartment. Do you think there's a tile-look equivalent of white oak? I still hesitate to put any wood-like LVF next to a real hardwood floor, though having it be a different plank size would help. If I tried a marble-look tile, what color?

In re: to what kind of blue, I like this overall look, including the two-toned floor, though not necessarily those colors. And sometimes when I think of blue walls, I wonder if I'm not designing a laundry room instead of a kitchen.

@Flo Mangan, I like the look of the TerraCore Nero you posted. For a rental, I suspect there may be concern a dark floor will show every speck that drops, but I have a dark cherry floor downstairs and it's nothing a quick Swiffer sweep can't fix. I guess my concern would be that it's too dark and will "shrink" the room. I also need to consider the floor extends into the hallway.

@Valinta, how light a backsplash do you think I could get away with without blending too much into the white cabinetry?

For reference, I found this wood panel room photo in another thread. While not identical, this is essentially what the living room connected to the kitchen looks like. It's not an open space, just a doorway, and the wood is actually in very good shape.

Basically, I guess I need a kitchen scheme that won't feel like someone is walking into another house when coming out of that kind of room. (The rest of the apartment is white with wood trim.) What I'm getting is that gray either in the flooring, countertop, or wall would be too jarring in this general area. I'm pondering maybe a light oak floor, black countertop, and maybe blue either in the countertop or accent wall. If I do that, I don't know what I'd do about the backsplash. It does feel a little like I could get away with a bolder, brighter color because of the wood paneling, but I don't want anyone to feel like they're living in a Crayola box.

The nuclear option is to do whatever I want in the kitchen, redo all the floors in the apartment, and paint the wood paneling white, but changing 500 square feet to accommodate 220 square feet seems silly.

Seems like a country kitchen is timeless AND appropriate in an old home... the flooring could be striking in black and white checkerboard layout of very simple(affordable) tiles ... white cabinets.. with black counters... for the backsplash ...paneling similar to the other room...... this will be bright and fun while relating directly with the adjoining room

JR-I understand your concern on the black style flooring but these are veined like marble and hide little things. I could envision a wood sided island setting on the black veined LVT with white cabinets except one cabinet would be an antique armoire painted a sage green. This could be a pantry with a coffee station or baking station. It would be signature piece and make a statement!

There are ways that you can incorporate darker elements to still have a fresh, even "cooler" toned look without clashing with warmer tones. You may want to look at elements of the rest of the space that you like and see where you can draw from those. Often times darker accents can actually give a space depth and won't make it look small like many people fear it will.

Here are some ideas using some repurposed furniture and materials which would marry your vintage home with some modern touches.

I love the styling and paint colors in this kitchen. Scaled for your space this is gorgeous.

Opps

A kitchen has a purpose and, unless it is part of a great room or family room, having the kitchen suit your purpose as you will use it is all the "fit' it must have -- as long as it fits your personal taste. That said, if you are choosing a warm vibe for the rest of the home, I strongly suspect you will be dissatisfied with the "cooler" kitchen after the novelty of having a new kitchen wears off. Would leave the "cool" "cold" looks for modern homes and lean toward a warmer vibe for the kitchen -- much prefer the more neutral and warmer vibe of the second kitchen pic ( in your original post ) for a house with an overall warmer vibe.

@JR Your blue inspiration photo already has warm wood in it. Look at that shelving and see how it goes up against the blue wall. Looks great. I do think black countertops with that dark of a blue elsewhere will be color overkill, especially if you want to add a colorful backsplash.

Painting the wood paneling could turn into a nightmare years on down the road if the paint flakes, cracks, or otherwise doesn't wear as well as the wood with clear coat that you currently have. Especially for a rental I would keep the wood with its original clear coat so I could just wipe it down after each renter rather than having to repaint after each renter.

I used a marble look-alike tile called Thassos from Porcelanosa for my own kitchen remodel, and the tile sits right next to dark wood pattern LVP and looks beautiful. It is almost pure white with just the faintest of gray veining. You could use something like that with a very faint gray accent, but any major input of gray into your area is just going to look out of of place with so much other warm wood around. Stick with those blue tones for your major color element, and it will come together better for you. If you like a two-tone floor, you could even bring your dark blue in there with a patterned blue tile. You can find wood look-alike tile, but the majority of people think it looks too fake to be desirable in most settings, especially when it adjoins to real wood.

Since you have white elsewhere, I think you could bring some white into the kitchen area, but how much would be up to you.

Sarah Richardson is singing the praises of mixed warm/cool tones in a room. Perhaps you should check her design sense out.

The fact that your overall house was built in 1920 isn’t as relevant as that it seems someone installed a lot of mid-century wood panelling upstairs much later to make that apartment. I can understand you don’t want to change the wood-paneled room, but almost whatever you do in the kitchen is going to feel like walking into another house unless you continue a mid-century vibe — concrete and frosty blues and aluminum in the kitchen.

Still might be the simplest thing to do is carry through with unpainted wood on the lower cabinets

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Or maybe this would work if you want paint on the cabinets, but note how much the darker blue is off-set by frosty blue

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Since you’ve already bought black appliances

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I think this looks great but maybe a renter would flee

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Red rustic is my fav...but probably not what you're looking for.

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These seem to marry warm and cool, "modern" and vintage

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Marmoleum works very well in 1920's houses.

If you want white countertops, choose that and consider whether wall paint or backsplash might add just enough warmth to suit your usual taste.

As a renter I would prefer to choose my accent colors and so might nor like the blue. keep it neutral and wood.

checkerboard floor is versatile

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I agree... checkerboard floors add a lot of personality with the least amount of investment

We just put a vinyl checkerboard floor in our kitchen in our 1895 house. We have unpainted wood trim and hardwood floors in the rest of the house and really didn't want a modern kitchen look at all. It was inexpensive and easy to put down. I'm sure something like Marmoleum would have looked better and would be more durable, but this was pretty decent and in our budget. Our kitchen is still a work in progress, but here's a pic of the floor.

@Quentin Parker Marmoleum might have looked better, but vinyl won't stain or tear as readily as Marmoleum will. Anyone seriously considering Marmoleum should do a deep dive into reviews of it first. It was all the fad on GardenWeb ten to fifteen years ago, but other flooring materials have since become more popular.

@Aglitter Yes, several people mentioned their bad experiences with it when we were trying to decide what to put in. We have a large dog and wanted something that won't scratch really easily. We haven't had ours long enough to know how durable it is, but it's cheap enough that if a few tiles are damaged somehow it wouldn't be a big deal to replace them. (That's another advantage of tiles to sheet vinyl aside from being easy to put down.) We're pretty happy with it, though my wife complains that it shows a lot of dirt and that she's had to scrub it more times already than she ever did with the old green linoleum in a year.

The floor ended up looking a little too new for my wife's tastes (maybe the colors?), but she's gotten used to it. I think Marmoleum has a better vintage look. Also if you go with a checkerboard floor, laying it in a diamond pattern is more work but I think it ends up looking a lot better.

Maybe smaller squares would be better from the cleaning aspect.. especially in smaller kitchens..I like the diamond layout, too.. as in any cost conscious choice a clever layout adds more interest too

I might also consider a more fun color on the base cabs in situations like this.. a pale aqua? Light loden or green?