Visited the area last summer. We stayed in Rapid City, which may or may not work for you, but we found it to be quite a nice small city - vibrant downtown scene, and a basement/rathskeller kind of place with extensive beer selection and superb pizza. Don't remember the name, but go to the main drag & you'll find it.
At Mt Rushmore we made the mistake of paying to park in the parking garage; the park itself is free, but $10-12 for pkg for the hour or so we spent in the main viewing area seemed a waste. When we left we discovered that excellent views were to be had from the roadside a short distance from the main site. Rushmore is iconic & I'm glad we saw it, but for me once is enough.
Nearby, we found Devil's Tower (WY) to be truly amazing. Even closer, you really shouldn't miss Custer State Park, a huge area of stunning (and many very different kinds of) landscapes and wildlife; I would make the trip again just to explore more of the park.
Also nearby (relatively speaking--this is the West) Badlands NP is amazing.