Having grown up near Yellowstone, I have to recommend going there. We went every summer! Also look into going into Grand Teton Park, Jackson, West Yellowstone, and into Cody, WY. Cody has the Buffalo Bill Museum which is a lot of fun.
Driving to South Dakota Black Hills would also be a lot of fun for your kids. The drive out there would be just as fun. There is the SPAM Museum in Austin, MN. Sioux Falls has a nice little zoo and some other fun things to do. There is the Corn Palace in Mitchell and also a dinosaur excavation site. The Akta Lakota Museum in Chamberlain has a fabulous little Native American museum out at St. Joseph's Indian School. And you have to stop for pie at Al's Oasis just across the Missouri. Wall Drug would be a fun stop for your kids and you can drive through the Badlands. Once you get to the Black Hills there is a ton to do! The Journey Museum in Rapid, Bear Country USA, Reptile Gardens, the 1880s train in Hill City, Keystone, Mount Rushmore, Crazy Horse Memorial, the Mammoth Site, and a ton of other tacky tourist places to stop. If you were to take the short drive into Wyoming to see Devil's Tower, there is a nice fish hatchery in Spearfish. You just don't want to take this trip in August when the Sturgis Bike Rally is going on. You won't find a place to stay and traffic can be horrible with all the bikes!
I also love Chicago and Seattle. We went to Myrtle Beach a couple of years ago and loved that. Although in early June the humidity was awful! We also had a great time in San Diego and enjoyed Philadelphia too. We are actually going to Washington, DC in a couple of weeks. My brother and his family live there and they love all the things that there are to do.
Feel free to e-mail me if you want more info on any of these places. I've lived in both Wyoming and South Dakota so I might be able to tell you about some places that you might want to avoid or places that you might not hear about otherwise.