The Badlands and Nat'l parks are definitely going to be worthwhile places to add to your trip. You will certainly enjoy it a whole lot more if you wait for the visiting crowd to leave. Not sure when your last visit this way was but just so that you know, Rapid City has grown significantly and is pretty overcrowded year around.
The real attraction around here is the scenery and usable forestry, a lot of the tourist traps are money grabs, nothing can top the hills themselves and that is what this place is really all about. It's just too amazing for words. Since you are an animal person (assuming) then a trip to Reptile Gardens may be in order, and the crystal caves are pretty cool too. Of course Mt Rushmore is a sight, and the roads around it are just going to make you wish you had brought your bike, I mean really wish!