I've car camped for 2-3 weeks total in the Bighorns, I've only backpacked one time.
It was out of West Tensleep Lake into Lost Twin Lakes. Wifey and I camped on Rainbow Lake and day triped into Lost Twin Lakes.
There is another trail out of West Tensleep Lakes that will take up to/around Mather Peak.
The Bighorns are incredible and only about 10 hours from the Twin Cities. Be aware that the mtn range is split into two parts "driving wise" and going between the North and South parts will take you around 3 hours or more by vehicle.
The fire tower (south half) is easily accessible by car and foot and is pretty cool. Drive down Crazy Women canyon, its awesome. We have stayed/rented the Muddy Guard forest service cabin a few times. Its only about 35 bucks a nite. No running water but it has electricity so you can heat up water on the stove and clean yourself.
I prefer the south half (everything I mentioned is on the south half) over the north half, less people and I think the scenery is better.
Check out the Occidental Hotel in Buffalo Wy, its free and very historic.
PM Pinetree on this site, he has backpacked alot of time in the Big Horns.
Buy this book.
Occidental Hotel West Tensleep Campaground I've stayed here a bunch. Sites are right on the lake and two trailheads start from there.