I haven't used them before, but we've been looking at the vanities from this company because they have a wide choice of styles and sizes in solid woods.
http://www.strasserwood.com/pages-prod/style&finish/choices-cab.html

It's always confusing to me when someone asks for "solid wood". As far as I know, true solid wood has not been used in many years for making furniture or vanities. There are components on furniture or cabinetry that are solid wood, but not the box. Most quality products are made with what is called furniture grade plywood - this is true for production items as well as custom made cabinetry. It is a wood product. It can be purchased in 5 ply or 7 ply. The outside layer is a high quality veneer and can be purchased in many different wood species.

The link that feeny has provided is to a company that uses a furniture grade plywood box as I described above which is a good product. What consumers should be concerned about is particle board (also called furniture board) with an applied veneer, which is not as good. A cabinet person told me the other day that there is a particle board that is being used for cabinetry that has the wood veneer on the side and they are allowed to market it as a "wood cabinet". Doesn't seem right to me - this makes it very confusing for consumers to tell what quality they are buying.

Yes, it is the cabinet door fronts that are solid wood and the box frames furniture grade plywood on the link I provided.

I would like suggest you these models of bathroom vanity manufactured totally in solid wood. We have three measures: 32",39" and 55" with double sink.
Designed and manufactured in Spain.