I have an outdated vanity. What can I do to cover the white top?

Paint or contact paper!

I've used the counter top paint and it's a job! But if you're up for it just make sure you remove the sink and fixtures. Using tape to block will not give you a nice edge. I'd tile it using 24x24 granite tiles. You'll still need to take the sink and fixtures out, but the look is great and granite can be butted up to one another with just a slit of a group line. One of the big box stores will rent you all the cutting tools (even for the holes for the fixtures). Just make sure and use the wet saw.

Unicorn spit sealed with famowood epoxy! You could spray it on and make it look like granite but in colors you've never imagined before. It's absolutely beautiful and so easy to do.

I painted mine, using acrylic paints purchased from Hobby Lobby. We replaced the sink and faucet, so I only had to tape along the walls. I then sealed it with 3-4 coats of a clear sealer (can't remember what I used exactly...a polyurethane of some type). It turned out great! It was easy, although took some time for coats of paint to dry and coats of sealer to dry. Luckily, this was not our only bathroom.

I honestly think that if you painted the wooden part of the vanity and the blue strip on the front of the countertop, it would make the sink and countertop look great just as it is.