Hida Takayama is known for its history of woodworking, and apparently supplied carpenters to Kyoto when it was still the imperial capital.
That history must weigh on people's minds, or give them the hook for operating their tourist-oriented business, because frankly, I didn't see many interesting things. There were plenty of shops offering free edge slabs for tables, but kid-wise, most toys and furniture were some combination of tacky, clunky, and boring.
How boring, you ask? Well, in two days of searching, these kid-sized chairs were among the best-looking pieces I found. They're nicely finished, but the green one on the left was the only one I'd consider schlepping home.
I don't know who makes them; the shop, Mifuku, [美富久], is just described online as a souvenir shop. But Street View shows they come in natural finish, too.