Tile the whole wall behind the vanity. If you want/need to replace the vanity in the future, you don't want a hole that may be an odd size to fill. Same reason you run the floor tile under the vanity.

It is more the side of the vanity I'm concerned about than the back. I have a window on the side and I'm tiling under the window and then it runs into the vanity and I think it looks better to have the tile on the wall before the vanity is placed.

Just to be clear, you are saying to tile backspash all the way down to the floor behind the cabinet? I'm guessing you would recommend tiling the side walls also before placing vanity?

If I had a vanity, and only had a backsplash to tile, I'd install the vanity, then the counter, then the backsplash. If I had the wall tiled, either a wainscot or a full wall, I'd tile first then the vanity, regardless if it was the side or back of the vanity.

What enduring said.

I agree to tile behind the vanity. I am planning our upcoming bath remodel and this is how I am thinking about the tile and the vanity: the vanity I put in now meets today's needs. There may come a day when I need wheelchair access and the vanity may be too much in the way. In my case, the sink I am using can then be hung on the wall. Others may find that they might want different changes down the road. By tiling the floor and the wall, you retain the ability to make changes to the bathroom. Get a smaller vanity and add a bidet; get a larger vanity with room to do a diaper change - there are a world of possibilities.