Black Hills National Forest
Mount Rushmore National Memorial is a short drive away, and so is the even larger Crazy Horse Memorial (http://www.crazyhorse.org/).
Rapid City is a transportation hub for the region. It has a few museums, and plenty of cheap hotels and restaurants chain and local.
Sturgis, roughly 12 miles to the East of Deadwood, is the home of the famed Sturgis Motorcycle Rally in August.
Wall South Dakota has Wall Drug, whose ubiquitous signs will be more than familiar to any visitor driving on Interstate 90.
Yellowstone National Park is just under 500 miles from Deadwood and 10 1/2 hour non-stop drive.