I can’t seem to find anywhere that sells 1/2" solid hardwood. It’s always 3/4"
Have you tried http://www.woodnshop.net ? I’ve been using them for 1/8 & 1/4 materials but they do have 1/2 as well with lots of varieties. I’ve been happy with everything I’ve gotten from them lately.
Rockler and Woodcraft both sell hardwoods in various thicknesses and lengths (down to 1/8" thick, though a lot of the pieces I’ve seen are twisted/warped). Some of the brands they sell (esp. when it comes to exotic stuff) can also be purchased directly from their own online stores, which will get you a better deal depending on how much you want (I thought I had at least one of those written down, but can’t find it now).
My local OSH has 1/2" and 1/4" oak planks, but stock varies by store.
OSH also has a consistent supply of 1/8" and 1/4" basswood and birch plywood. Decent quality and the price is similar to what I’ve found online.
my goto for hardwoods is http://ocoochhardwoods.com
they have from 1/16" to 3/4"
also a good source for baltic birch plywood
Mine has not arrived as yet but they have a lot of stuff at decent prices. My goal was thinner and wider with a dash of exotic, and 12" wide 1/16" thick mahogany does fill that bill.
I’ve seen 1/2" boards in I think four different species at my Menards. They are a regional version of Home Depot/Lowes.
I’d also suggest looking for a local lumber shop. They’d be able to mill down whatever you’re looking for.
For questions like this it would be extremely helpful to know the geographical area where you are based.
Aside from that search for hardwood dealers as those places would be suited to resaw thicker boards into thinner ones or to plane them down. If not available rockler and woodcraft or hobby stores should have thinner boards but not great selection. Otherwise online sources abound and you could shop around for best prices.
I tried Ocooch Hardwoods a few years ago for a small selection of 1/8" stuff. It all arrived pretty badly warped and, their customer support never responded to my complaints. YMMV.
Every piece I’ve gotten from green valley has been really nice and flat.