If you just want to see Mt. Rushmore, it's basically a day trip. You'll spend about three hours at the park.

If you're looking to stretch out your trip you can easily spend 3-5 days in the Black Hills area. Other parks worth visiting including Custer State Park (1 day), Jewel Cave National Monument (1/2 day), Wind Cave National Park (1/2 day), Badlands National Park (2 days), and Devil's Tower National Monument (1 day including drive there & back).