I am fortunate to have a really great lumber company in town. They have a mill shop that has hundreds of trim and molding pieces in all the popular hardwoods. In addition, they carry about 10 or so different plywoods with hardwood veneer. Depending on where you live, I would think you should be able to find a store that has a good selection of hardwood ply.
This summer I built a maple cabinet for my shop. I looked at birch, which was about $50 a sheet for 3/4" thickness. The maple was within a dollar of the birch, so I got it. The cabinet is open, so the face frame cost negligibly more than the poplar I was planning to use.
For walnut, cedar, mahoghany, and other more "exotics", the prices ranged from the $60 range up close to $100.
BTW - my wife questioned why the shop cabinet is nicer than most of the other cabinetry in our house. And that comment helped me justify getting a track saw last month, so I could build new cabinets in the rest of the house. I think she bought the rationale ... [wink]
Of course, I now need a Domino for the joinery, and of course a Festool sander, and ....