I highly recommend you clean the floors FIRST and then decide the wall colour. I have a sneaking suspicion that you will have a VERY different colour once it has been cleaned. Once they have been cleaned, I recommend you LIVE with the colour for a few weeks to get used to it. At that point, you can pick a wall colour. And remember the cleaned tile will throw a LOT of WARM colour into the space and onto the walls. The 'warm' white may turn a VERY strong colour with all that warm orange being thrown onto the walls from the floors. You will notice many inspiration photos have CRISP white on the walls.

The first thing that came to mind for me was the light fixture. Do an online search for "modern pendants" and you will find something more MCM for the look you are after. Another great thing that is very mid century is to look for a brutalist sculpture for that darker accent wall. MCM hardware is often antique brass, so let that be your metal finish guide when looking for a sculpture. Or, you could find a couple of very large black and white framed prints for that wall. Then maybe go for color on the drapery--or a large colorful print--that would add a lot of spice and interest to the room.

Sigh.. I have no idea what I'm doing wrong, but every time I try to reply, I lose the response. Hopefully 3rd time's the charm! Let me summarize even further now that it's my 3rd attempt - Thank you @Patricia Colwell!! I appreciate your response. I agree it is definitely a very formal set, and I'm not sure if I could fit it with the rest of the house, given I intend to have a more "casual" or "relaxed" feel in the adjoining rooms. I love the look of formal sets, but the rest of the house would be very informal. I'm not sure eclectic is the exact match, but I said that because I've been going through interior design photos the past few weeks, and all the ones I'm drawn towards have all been labeled "eclectic". I have 0 eye for design, though, so I would not go down the eclectic route, as I would definitely hit "tacky and bold" as you mention. Maybe my style is more transitional, but with a bolder color palette and a few older-style pieces, like antique-looking armchairs? I haven't pinpointed the common theme in what I like yet, but the "eclectic" (or whatever they really are) homes feel more "homey" to me, whereas modern just feels too staged for me personally. Looking through more pictures, I really like the legs in this set and the comfiness of the chairs, but I don't like the drapes, painting, or chair fabric/pattern - And I think the tables in these look really interesting, but I'm not a huge fan of anything else in the rooms -

You definitely need some art and/or wallpaper (I usually do not recommend wallpaper because I do not want to deal with it)! The room looks too boring and just needs some punches of color. Since your rug has some blue in it, I would play up the blue in art and wallpaper along with a cabinet displaying china or ceramics in blue! Here are a couple of my favorite dining room photos from Houzz (I love blue because that is the color of my dining room)!