I've been through Wyoming a couple times on trips to Yellowstone.
First off, Wyoming is not fun to drive through to get to a destination. It's very flat and very windy. But, it's great for just cruising. Jackson and Yellowstone are a must. Crazy stuff you'll never see anywhere else. Very minimum in Yellowstone is 3 days, IMO. Check out both loops, not just the bottom.
As for other towns in WY, driving through Thermopolis is awesome. Crazy land formations. Cody is nothing great, but an ok place to stop and grab lunch. Everywhere else is only good for getting gas. That said, I would absolutely love to own a ranch anywhere in WY and just live out in the middle of nowhere.
Let me know if you need any other info or tips in Yellowstone.