A standard vanity is 30 inches tall. I am also 6' plus, and agree they are too short. The human race has grown taller in the last 150 years, but vanitys haven't.
But if you make it 36 inches, some shorter people may think it is too tall. Although I know this is commonly done. I would build up a 2x4 frame on edge where the vanity is going to set. That will make it 33 1/2 inches which is a definite improvement. If you still want to go the full 36 inches, build up a frame with 2x6s on edge. Trim out the space at the bottom with 1/4 inch plywood stained or painted to match.