It should be about a day and a half's fairly comfortable drive to the Black Hills of South Dakota. Having been there many times I would recommend it for the kids as well. They can see Reptile Gardens on the south edge of Rapid City and of course make the tour through Deadwood and the President's Monument. You'll go through Wall Drug Store, which is worth a stop of a few hours on the edge of the Badlands. Be sure to take the family about an hour south of Rapid City to Hot Springs, SD for a tour through the dinosaur digs that are continually going on. There's Custer, SD and the various caves, including the largest one in the Black Hills, the Cave of the Winds. A drive down Spearfish Canyon (remember Dances With Wolves?) from Cheyenne Crossing to the town of Spearfish is very interesting.
Just west of Rapid City is the first National Monument in the U.S., Devils Tower, Wyoming. It's a few miles outside of Sundance, Wyoming and a beautiful drive.
This site might be of help:
http://www.blackhillsvacations.com/VacationPac kages/Index.cfm?utm_source=Google&utm_medium=p pc&utm_term=black+hills+vacation&utm_content=B hvacations&utm_campaign=Spring07
By the way, this is primarily a U.K. site. I hope you get some other answers as well...