The web sites cover everything pretty good. I'm not a golfer, so can't help you there. I do know that there are about 4 courses in Rapid City, and at least one at Spearfish.
Hill City would be a good central location. It's home to the 1880 train, one of the oldest steam trains in the country. Several art studios, gift shops and such. The Mickelson Trail runs through town, a great bike trail, if you bring bicycles. Custer State Park, Mount Rushmore, and Crazy Horse are all close by. There are a couple of good campgrounds there, I have heard the Rafter J Bar is nice, but haven't camped there.
The hike around Sylvan Lake in Custer State Park is a nice, scenic short hike. The trailheads to Harney Peak and Little Devils Tower are also near Sylvan Lake. Harney peak and Little Devils Tower are both great hikes with breathtaking views, but are 3-4 miles round trip and are more difficult.
Spearfish Canyon is a nice scenic drive. Deadwood is always interesting, seems like there is a golf course up there also. Deadwood has several special events and free concerts there during the summer, so be sure to check their sites for a list of happenings.
Ellsworth Air Force base (just east of Rapid City) has a free museum with several aircraft on display outside. They just added a B-1 bomber this week. Haven't stopped in there lately, but the parking lot is usually full in the summer when I drive by. There is also a former missle silo that is being converted into a park, near Wall and the Badlands, but I don't think it is open to the public yet.