Every 1/4" counts for a vanity.. Could most likely find something at a home depot or lowes. Tear out that hideous tile and paint the walls.

Ikea has a sink and cabinet that is 10 5/8" deep.
http://www.ikea.com/ca/en/catalog/products/S19894245/

ikea 179

I would recommend a pedestal sink and forget trying to do a vanity cabinet. If you find one in the correct shape, I would look for an oval it should fit nicely while not taking u too much precious space!

A dresser turned into a vanity is a relatively simple thing to Diy. Many dressers already come in the shallow depth you're looking for (search thrift shops or garage sales) and can easily be painted to match your color scheme. If you don't want to cut out a hole in the top for a drop in sink (which takes up drawer space beneath), you can opt for a vessel sink which sits above the vanity top. We're currently building a vanity from scratch using this pottery barn vanity as inspiration only with a vessel sink. We plan on painting it white and staining the top a driftwood color.

Isn't it good we are all different. I second the dura it suggestion, but I was thinking what great tile and original fixtures you have! In my market those would be selling points that would be emphasized not removed.

Darn auto correct. Duravit obviously!

http://www.apartmenttherapy.com/small-sinks-213814

do a small trough sink out of stone.

wow, im such a restore person and not a rip out person, I think the tile is awesome, the sink and the old soap and water cup holder.....people just cant find those anymore. I would say loose the wall paper. and keep the tile. and have a carpenter build you a counter.

I agree that if the tile is in good shape leave it. with the proper vanity (one needs places to keep stuff in a bathroom) and minus the wallpaper it could be beautiful

in the order of having a chest and fitting a vessel sink. all 15''d and less than 36" wide.

As others mentioned, not sure about your budget or your location, but Porcelanosa has large selection of wonderful, very small bathroom sinks (and with cabinets) because they deal with a lot of very old European bathrooms in stone buildings that cannot be easily enlarged. Do check out their web site: Porcelanosa-usa.com. Quality products, too.