The Black Hills are great! I've done a lot a field work there. Love the place. But don't go there right now IMO. Sturgis is just around the corner and there is bound to be about thousands of bikers all over the place. You will not be able to escape the sight and sound of motorcycles littering the cities and roads. So unless motocycles are your thing I'd recommend September in the Black Hills. Few tourists, the temperature is great. Fall comes a little quicker in the Hills then the rest of the Great Plains, so you'll have some nice colors as well.
You can hit all the places and then some that sd'sker mentioned. Though I'd skip on the Crazy Horse Memorial. It's not even close to finished so save your money IMO and look at it from HWY 16 between Hill City and Custer. Deadwead, the wildlife, the scenery, the caves (Wind Cave and Jewel Cave are fun), the small towns. There's plenty to do, especially with kids if you have any.
The only down side may be when you can or want to go. Like I said, I'd go during September. But then football season is underway, so the during the week (M-F) would be the time.