Wall, South Dakota. Wierd, check. Little, check. Tourist economy, check. Population under 10K, check. Treasure . . . er, well, uh, I guess that would depend on what one considers treasure.
I’ll nominate Saugatuck, Michigan. A quaint, artsy-fartsy town on Lake Michigan.
AKA “The Art Coast of Michigan”. TM
mmm
Nashville.
No, not THAT Nashville… Nashville Indiana. Right outside Brown County State Park, which is beautiful, especially in the fall. Nashville is a little tourist town full of unique shops and restaurants, with horse drawn carriages to allow you to tour in comfort. A beautiful little place to spend an afternoon shopping!
Cape May, NJ (see the 1800’s lighthouse and the old WW2 installations!)
Occoquan, VA (OLD OLD colonial riverside community close to DC)
Clifton, VA
Yorktown, VA
Harper’s Ferry, WV
Intercourse, PA
St Francisville LA - population in 2000 was 1,712. Absolutely beautiful and the Audobon Pilgramage is this weekend.
Danville PA - close to lots of things like Bill’s Old Bike Barn and Museum, Knoebels Amusement Park, and historic sights like French Azilum (probably the “French-est” place in the New World) and Fort Augusta. Its a really small town that basically supports a regional hospital which is why it has hotels and a lot of good restaurants.
Taos, New Mexico.
North Conway, NH (gateway to the White Mountains)
Maybe Newburyport, MA and Rockport, MA (if you’re into quaint seaside towns or birdwatching.)
Galilee is a little fishing village in Rhode Island. It doesn’t really qualify because its economy is probably mostly fishing, but it is interesting in that it’s not at all corporate-America-homogenized… it’s still totally local, pretty much just the way it was 50 years ago when I was a kid. It has a small beach (named after Salty Brine, a beloved local celebrity), a few little gift shops, a couple of good seafood restaurants (well, one good one anyway), and is the departure point for the Block Island Ferry. A local custom is to sit in lawn chairs by the Narrow River Inlet, eat take-out seafood (typically chowder & clam cakes) from the restaurants, and watch the boats come in and out.
Beat ya to it Skammer. 
Check post #44.
A couple Kentucky towns:
Berea — authentic crafts, small historic college where students make handcrafts in exchange for tuition.
Bardstown — close to many distilleries, including Maker’s Mark, which is cute. Also nearby is the Abbey of Gethsamani, where Thomas Merton lived and wrote (and is buried). Lots of B&Bs as well as My Old Kentucky Home State Park, location of the house where Stephen Foster penned “My Old Kentucky Home.” There’s an outdoor drama, too!
Cooperstown, NY.
This is pretty much the trope namer for this thread. Tourism is what they do. Whether or not they do it well is another point entirely.
It’s also the subject of the most gawdawful movie I’ve ever seen. The Myrtles plantation is supposedly haunted, which inspired some people to make a Blair Witch-type flick. The film is best missed, though I’m sure the area is wonderful in real life.
My nomination is Brownville, NE. Not as well-developed as some others on this list, I’m sure, but they try.
Technically MV is three towns. Or six, depending on how you define a town.
Rockport, MA is another one.