Mattyd, I'll share a few in our area (Big Horn Basin). Thermopolis - Top rated (in USA) privately owned dinosaur museum, Hot Springs State Park (thermal hot springs), 15 miles North toward Worland - then North-West on Gooseberry road will take you to some badlands ( looks like you just arrived on the moon). Meteetsee,Wy (between Thermopolis and Cody) - Really nice museum (very large grizzly killed just out of town), 15 or 20 miles west of town is the Pitchfork Ranch (were many of the Marlboro commercials were filmed), and from Meteetsee driving to the head of the Wood River will take you to Kirwin. An abandoned mining town, which you can only get to via 4 wheel drive/atv/horseback (and only then in mid to late summer - you cross river many times) Amelia Earhart fell in love with Kirwin, and was having a cabin built at the time of her disappearance. These a are but a few things just in our area. Get the book earlier mentioned - dozens of places we haven't been yet!
Enjoy Wyoming and Happy Trails! memtb