Not much in the way of car museums.
Pretty much all of the northern part of the state (Gillette excepted) is nice. If'n you don't cross the mormons. As stated earlier the drives through the bighorns and windriver canyon are nice. Cody and the northwest portion are decent.
If you drive south towards Casper out of the windriver canyon and take a left at Shoshone on highway 20 you will be as close to the middle of nowhere as you can imagine. There is next to nothing 'tween Shoshone and Casper. A good malt shop in Shoshone though.
If you're in the area:
http://www.wyomingtourism.org/discover_wyoming/events/more.php?id=2436
A little local flavor. Take some pictures of mullets for us.