Don't try to match. It'll just look like a bad patch. Make it look deliberate, treat it as a feature. Have fun with it. Create a border around the vanity and fill the remainder with mosaic tile in the colors of your existing tile mixed with colors of the rest of your bathroom. Make sure you remove enough old tile, linoleum or wood flooring around the new vanity to leave enough room for the border as well as some of the new fill tile to show. Just like with an area rug, you want to be generous in size. If you have beige tile and say, black accents in the bathroom, you might want to choose a solid black tile for the border, then you could use mosaic tiles in beige tones and sprinkel in some black ones to fill the rest. Alternatively, if you find tile that almost (but not quite) matches your existing tile, you could do the border in mosaic tile, or a contrasting rectangular tile and fill the center with the almost matching tile. I only advise you to do that though if the border helps to visually separate the tiles enough to make the slight difference disappear. The sky's the limit. Good luck!

I agree with Cpartist"s layout and like moving the closet over as suggested by D M so that bedroom 3 has easier access to the bathroom. Do you have room to have the toilet face the tub and add a linen cabinet next to the toilet? How wide is the tub toilet area?

If you're redoing the shower anyway (looks like tile and grout are degraded and may not be keeping moisture out of the wall), then a tub is pretty cheap, and you might be glad you replaced it rather than having to build your whole bathroom around the current shade of gray. Plus, it may look even worse once the rest of the room is fresh and new.

Do wall hung vanities I use Godmorgon from Ikea and to be safe I usually put legs about half way back you do not see them but they are good for extra support and I would do that in a rental for sure. Probably IMO a gut job for the bathrooms and new acrylic shower stalls just to make sure there are no issues with anything leaking . Not sure what the budget is but a nice neutral fllor and wall tiles will make renters happy. BTW the Godmorgon can be bought with the counter and sink all in or you can do your own counter and sink