I live in Rapid City and have two kids, 2 and 5. I can tell you a few things about what we do (Sunday Funday - we pick something fun to do as many Sundays during the summer as we can).
Blackhillstourism is a great resource, and thet have a great app that can really help along the way.
Mt Rushmore: is a must-do, for any age.
Crazy Horse: meh. That's really all I can say about that.
Custer State Park: certain must-do. If you like horseback riding, Blue Bell Lodge is the BEST. The Wildlife Loop is great, and if you like hiking, the Lower French Creek Trailhead shouldn't be missed.
Hiking or Biking: the Mickelson Trail is a great find. It follows an old railroad grade, so it's never too steep, but it's very scenic. It goes all the way from Deadwood to way south of Custer, but my favorite parts are around Hill City and Mystic. You can also rent bikes at a couple different places and go down the trail.
If you are a hardcore hiker, the Centenial trail is great.
And the Spring Creek Trail head is a site to see. It's an easy hike, but you go through old tunnels left from the mining days.
If you are into kayaking, you can rent kayaks in Rapid City (Global Market) and head out to Rapid Creek - which is also great to tube down.
Keystone: the taffy shop and fudge shop can't be missed. For something a little different, try the zip line. It's a blast.
1880 Train: My son LOVES this and we go on it at least a couple times a summer, and then again at Christmas to meet Santa. It's a nice relaxing ride that takes you places you don't normally see, and it has a lot of history.
Helocoptor tours: If you can swing it, it's great. It's actually not that much either, especially compared to Disney.
Caves: I think that Wind Cave is the best. It's owned and run by the park service, not a private owner, so I think they do a little job. Plus, Wind Cave Park is a must-see.
Deadwood/Lead: touring all the hot spots - the cemetary, the museums, ect is always good. My son loves to gold pan at Broken Boot. They also like Gulches of Fun.
Spearfish: Drive through the Canyon. See Bridal Veil Falls, see where the gigantic boulder rolled down the mountain (which landed so hard it registered on the richter scale), see Savoy and where Dances with Wolves was filmed. Another must do is to visit one of the Fish Hatcheries. There is a Historic one in Spearfish and a more up to date one in Rapid. they are educational.
Another thing that is worth it is Summer Nights in Rapid City, or just walking through Main Street Square. Thursday is the festival night where they have street vendors, live bands, and other events. But any time is a good time to see it. They have a fountain park which my kids love (bring a spare set of clothes for your kids!) and they have some neat shops - ice cream, a soda shop and a couple good restaurants.
Trout Haven is a fun place to take kids fishing if they have never fished before, or even if you do fish. And if you want to, they'll even cook cook what you catch. Oh, and right by Trout Haven is the Sugar Shack - the BEST burgers around. I ride my horse up there often. It's soooo good!!
There are a couple good places to rent ATV's if that's your thing too. Deadwood has Mad Mountain which is good, and there are a couple in Hill City.
Restaurants: if you are in Rapid, the Firehouse, Botecceli's, Engima, and the Cornn Exchange are all great choices.
Hill City: Alpine Inn is always good, and Slate Creek Grill usually delivers
Keystone: Ruby House and Grizzly Creek, and of course Silk Fudge and the Taffy shop.
Deadwood: If you want a great buffet of steak and crab, Silverado is probably the best in town (fri and sat). Also, you can never go wrong with Jakes. It's Kevin Costner's restaurant and it's pricey. But, I have never had a bad meal there.
Spearfish: Guadalajara's is the best mexican around. Seriously. We drive from Rapid to eat here. Also, Roma's is awesome. Also another we drive from Rapid to eat at.
that's all I can think of for now, but feel free to ask me any questions. I have lived in the area most of my life, we spend as much time as we can in the hills and I worked for SD Game Fish and Parks in college, so there are very few places I don't know.
Custer State Park, Needles Hwy, Mt Rushmore(day and night on different days) 
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