Any color at all will go with your white. What color is a featured color in other rooms? Do you stick to mostly neutrals, or do you have bold or pastel or grayed accents elsewhere? I would paint the vanity according to your house’s decorating scheme and do a non-white counter, then use those colors in art and towels in the room.

I think the cabinet's wrong for the room. I like the cabinet better turned sideways, but that creates an odd empty space beside the toilet. Could you find a wider-but-shallow china hutch at a thrift store? Preferably without glass doors. They're easy to find these days. Something that would fill that back wall. Consider painting it white to match the vanity ... or go with a color. Use dark hardware to match your faucet. Then fill it with pretty towels (not white -- bring in some color), small plants and such. With that done, add a large piece of artwork over the toilet and a pretty floor mat (those big tiles aren't doing much for the room, but taking them out would be real money, and it'd turn into a snowball project).

Try bright colors. The navy rug isn't bad at all. Also test out turquoise and different greens. Wallpaper can be a good way to blend pleasing colors into a bathroom with blah tile, and you have so much tile that you can get pretty wild with wallpaper without it being overwhelming. If you decide on wallpaper you can repaint the vanity a crisp white or something from the paper. (Keep the groovy knobs.) The mirror fits the bathroom if you want to keep it "authentic" (which is probably the way to go when keeping tile like this). The light fixture not so much! (Nor the sink...but sinks are more of a hassle to replace than lights.) I'd look for something retro (keep it chrome) and simple sort of like this: https://www.lampsplus.com/products/george-kovacs-saber-20-inch-wide-chrome-bathroom-light__h7689.html How bad is the floor? It looks like it might just need regrouting, but I believe you if you say it needs to go. Trust Palimpsest on floor suggestions.

I love the look of the dark floor Sabrina posted. But…a lot of things end up on a bathroom floor that might or might not be visible on that floor. Skin flakes, hair, nail file, skin care products, water drops/mineral content. Evaluate your situation. But, it sure looks good clean like the photo.