If you can get a day or two to visit Yellowstone you would find it wonderful if this trip is in June there will be lots of baby elk and bison. Devil's tower and Rushmore don't take much time to visit, once you get there. Badlands time will depend on how much hiking you want to do in the park.

Hope you have a fantastic trip.

If you have the time, try to stop at Fort Robinson State Park (it would be on your way, more or less, from Grand Island to Mt. Rushmore). It's beautiful, historic, and you can even stay in an old officer's quarters building.

You could stay in Cody WY..fun place and about 45 minutes into the East Entrance of Yellowstone. You could do a daytrip loop if you don't want to do all of Yellowstone. Altho if you have time, you coud go all the way south into Tetons..my favorite area...but might be too much this trip.

Pugsley, there is more to the Black Hills than Mount Rushmore. The Mount only takes a couple of hours, check out Crazy Horse Monument and the museum on the grounds. There is lots and lots to see, just depends your tastes.

You might read day 3 and 4 of DW's trip report from Nebraska to Mt. Rushmore, Custer State Park, Devils's Tower, etc:

http://www.fodors.com/community/united-states/how-many-western-national-parks-can-we-see-in-2-weeks-710-2509.cfm

Thanks so much for the replies!

Grand Island to the Black Hills/Devils Tower area will be a good 8-10 hour drive. I would try to stay someplace your first night in the Black Hills, (Rapid City is on I-90, lots of places to stay there) and the next day do Mt. Rushmore, Crazy Horse, Custer State Park, etc, (not sure what exactly you want to see in SD, do a search on this forum about the Black Hills to get ideas). If you get time, it would be fun to go to Hot Springs, SD and stay overnight there, too. They have a natural hot water pool, very relaxing. You could visit the Mammoth Site there too. From Hot Springs, I would go back North and take I90 to Devils Tower, it won't take long to see that maybe 1-2 hours tops. After that, venture over to Cody, WY, and maybe stay there one night. Cody has the Buffalo Bill Center, it's a very interesting museum. The next day Yellowstone (my favorite place in the world!!!) would be an enjoyable drive. Labor Day is great for visiting Yellowstone, most of the crowds are gone. It can get chilly at night, so bring a jacket! If you don't want to stay in the park, try to get over to West Yellowstone or Jackson Hole. Jackson Hole is beautiful, but pricey. You should definetely see some animals here and there in that part of Wyoming.
After that, you will be probably ready to head back towards Nebraska, so you might enjoy the Big Horn Mountains. Buffalo is a cute little tourist town, it's very close to the Big Horn Mountains. A beautiful drive for sure. If you want to see more historic things, drive down to Casper and see the National Historic Trails Museum, stay over night there, and you could make it back to Omaha in a day. It will be a long drive, but it can be done.

Word of warning, Wyoming does not have a lot of places in between to stop at. So plan accordingly, keep beverages and food in your car and map out the rest areas. Cell service can be spotty in areas too.

I hope you have a wonderful trip!

Labor Day week should be great weather for you. It's about a 2 1/2 hour drive from Omaha to Grand Island. If you get in early enough you may want to stop at the Durham Heritage Museum, The Joslyn, or Henry Doorly Zoo before starting your trip. The Nebraska State Fair is 8/26- 9/5 right there in Grand Island so you may get to attend!

You'll be taking I-80W from Omaha to GI then US83 and I90 to Mt Rushmore I would think. Stopping in Valentine would be a good break and beautiful. Coming back it will mostly be I90 and I29. Along with all the other places suggested Rapid City would be another good stopping point. Have a great time.