My wife is from Deadwood, SD, and we go back there often to visit her mother, who now lives in Sturgis, SD, home of the famous Harley-Davidson motorcycle rally. If you are going to do the Black Hills, I really recommend flying into Rapid City -- it doesn't make sense otherwise. I highly recommend seeing the South Dakota caves that are run by the National Park System, i.e., Wind Cave and Jewel Cave. I also recommend seeing Deadwood if you want the Wild West thing. There are enough authentic things to still see there that the gambling hasn't ruined to make it worth your while.
You asked about hotel stays with Hilton, etc. Rapid City and Deadwood have Hampton Inns. We have stayed at the one in Deadwood and recommend it -- I posted a review of it in the Hampton Inn review thread in the Hilton forum.
It is a fun drive from the Black Hills to Yellowstone -- fun because every conceivable route has signs from the local tourism promotion folks trying to get you to drive via their town. The signs claim that going via Route A is the "shortest route" while the towns along Route B is the "fastest route" and the folks along "Route C" want you to know that their way is the "most scenic". Personally, I recommend going via Newcastle, Wyoming, and stopping by the Blue Moon Boutique there and making a large purchase from their extensive selection of authentic western art. (Why? Because a sister of mine is a part owner of the gallery.) <grin> Truthfully, however, they do have the fair dinkum article, unlike many stores in the Black Hills that sell only tourist kitsch.
If all you want to do is Yellowstone, then I recommend flying into SLC instead of DEN, or into Idaho Falls, ID, or Jackson, WY, if you have the money or miles to burn.