You really can't go wrong anywhere in the mountain parts of MT or WY. I spent a couple nights camping along Grey's River Road outside of Alpine, WY and two more along the Upper Green River outside of Pinedale in October. Both were lovely. It really depends on what you're looking for. For more ideas, check out the Walthall Family series from
Expedition Overland. They spent a couple months exploring Montana this summer.
A couple places to check out for a change of pace along the way:
Buffalo Bill Center of the West in Cody, WY: You can easily spend a full day here. There are five different wings to explore.
Museum of the Mountain Man in Pinedale, WY: Good for an hour or two depending on how deep you want to go.
Once you have things narrowed down a bit, call the local ranger stations and ask their advice. I did that several times on my last trip and found them to be very helpful.