Thanks very much for all your help Susan! Yes, something like that would have been perfect. I even found another site where I could have custom-ordered the size, the trim, everything.... but then I remembered.... ;-( Part of the reason I made sure I got a new apartment that had a balcony was...I like being able to let my two cats out there (I will have a screen enclosure built around the entire balcony....). And one of my cats is ex-feral, and has always had random peeing issues. He likes to pee on plastic bags and...he used to sometimes pee on my outdoor doormat. So I suspect he'd use any type of outdoor rug in this same way. And while it occurred to me that I could hose this rug down, it's just not that easy to do when you live in a 4th floor apartment in the city, nor would I feel like carrying a full size rug in from the balcony to say clean it in my shower.... So....I think I will unfortunately have to forego the rug. I'll just have to live with my cement balcony floor, for as long as I'm still living here. (It's only supposed to be a temporary rental only...maybe 2 years....) Tx!

Of course but before doing it are you sure you want all those shelves to fill with a bunch of “stuff”I would remove all the shelves then I think thosecabinets can easily be taken out install the new floor hang the TV on one side and art on the other and keep the lower portion of the cabinetry for storage and of course to hide all the wires for the TV and all the other stuff that goes with the TV.

Do nothing...and install the LVP as-is. The terrazzo you have is a HIGH VALUE floor. I mean SUPER expensive to duplicate. I would 'give up' on the warranty of an LVP floor and just toss it in. To do anything to this floor will ruin it for future generations. To level it you would have to grind, grind, grind, grind to get SLC to grab. Once you do that, you have lost the value of the item. At that point, you might as well spend the $3/sf to jack this out. It will be worthless. The TILE is see in the background can be left in place, you can do a bit of grinding and then fill the grout lines with SLC. You need to do some scarification of the tile to get the SLC to GRAB the tile. So long as it grabs you can fill the grout lines and flatten it to the best of your ability. I would EXPECT to use T-moldings where the two floors meet. The only way to avoid this would be to remove it all. In essence you are covering the HIGH VALUE products with a lower-value product. I get it. The current floors are not very attractive (compared to today's trends). But realize the value of the terrazzo. If you were to replicate the floor today (with modernized product) you would be looking at $25-$30/sf. Compare that to the $4/sf product you are going to cover it with. Right. LVP is a downgrade compared to terrazzo. No way around it. I would leave the terrazzo in tact and untouched. I would give up on any warranty and install the LVP over top. The tile can be dealt with as you wish. But remember to put in t-moldings between the LVP sitting over the terrazzo and the LVP sitting over the tile. NO underlayment. Most LVP's do NOT allow underlayment. Especially if they have attached underpad. This is LVP not laminate. If you want to get a cork underlay on these floors to help even out the surface then work with $4/sf laminate. That will buy you a TOP OF THE LINE European laminate. You can then use 6mm cork to correct some of the unevenness. But LVP will not allow that type of underpad.

Luxury vinyl tile that comes in planks can mimic stone or porcelain tile as well as wood. That would look better than having something that looks like wood, but isn't wood, next to real wood. You could have it laid in a herringbone pattern which would contrast nicely with the wood flooring. One of my friends did this when they remodeled their kitchen recently. I assume you're interested in LVT because it's softer than real tile. As the poster above says, many people now have real wood in their kitchens. However, we moved into a house recently that has wood floors in the kitchen and I don't like it. I never feel like I can get it as clean as tile because you have to clean it gently so you don't damage the surface. We did put LVT in the finished basement and I like it there. If I were remodeling my current kitchen I would go back to ceramic/porcelain tile. But some people think that is too hard. I don't do elaborate meal prep, so I am never standing on the surface for long periods of time so that never bothered me. Go to a good flooring store that has lots of options if there is one in your area and take some time to think about what you really want and will look good with the rest of the kitchen.