Sorting through the advice you've gotten so far, there are still a few points that you might want to consider as well. First off is your choice of gateway city. Chicago could work either with a two-and-a-half day drive to Yellowstone or with a (relatively expensive) internal flight to a small northern plains airport. Personally, I'd probably choose Denver for a couple of reasons: First - there are direct, non-stop flights available from London via British Airways; and Second - it would allow for a great internal loop trip that took in Rocky Mountain National Park, the Badlands and Mount Rushmore, Yellowstone and the Grand Tetons, and the spectacular Bitterroot Mountains and Great Divide Basin on the return to Denver. That would allow you to spend 4-5 days in each of three great locations and have a doable day's drive between each of those stops.

I will also note that Buffalo Bill's grave is in Golden CO just outside Denver, and the home of 'Unsinkable' Molly Brown (of Titanic fame) is in Denver proper. Both are open to the public and there is a small museum associated with Buffalo Bill's grave and guided tours of Molly Brown's home are available. Also, if it's of interest to you, the Stanley Hotel in Estes Park CO at the entrance to Rocky Mountain National Park was the inspiration for Steven King's The Shining.

Then besides Mount Rushmore and Badlands National Park, other attractions in the Rapid City SD area include Wind and Jewel Caves, the Crazy Horse Memorial, and Devils Tower. A word of caution though, there is an annual motorcycle rally in nearby Sturgis SD every August and the roads and accommodations in the area can get a bit overwhelmed for a week or so before it starts until a week or so after it ends. So you may want to time your travels to avoid that period. Remember that one of the beauties of a loop trip is that you can do it in either direction.

Native American Reservations will be scattered throughout your travel area but a few that are worth looking into would include the Pine Ridge Reservation in southwestern South Dakota which has been the scene of some unfortunate history but welcomes visitors to its interpretive center in Kyle SD just south of Badlands National Park, the Wind River Reservation between the Grand Tetons and Denver which does not have a visitor center per se but encompasses some of the most scenic country in Wyoming, and the Crow Indian Reservation in south-central Montana which contains the Little Bighorn Battlefield, site of Custer's Last Stand.

AZBuck