I agree to start with painting the vanity first and maybe adding some doors to hid the pipes. If you aren't handy, a finish carpenter or specialty cabinet shop could help for less than to rebuild the equivalent. You could replace the top cabinet doors with Shaker style doors to match the bottom if you wished, but that is not essential. Old style kitchens and baths had a sort of shaped door over the pipes that might work here too and repeat the curve of the upper doors..

If you got some spare tile, you could take that to the store to figure out paint options. It definitely has a pinkey beige caste I think with brown and terra cotta, and the sink is more yellowy/orange. A dark brown finish could work to minimize those differences, or a slightly creamy antique white perhaps with the walls and door repainted to match. It will be tricky to get the exact right color of off white. It could be the lighting too. I think more simple and chunkier hardware could look good too.

If you are keeping the tile then definitely stain cabinet darker. But may want to also consider changing out the tile.

Wouldn't it be cheaper to replace the vanity than the tile? We really dislike the vanity, especially the cabinets on the side of the sink .... it's a really odd layout and its all very scrunched.