It's been awhile since I've frequented out west normally, but...
Since you'll be on the west side (in no notable order):
- "M-Hill" - Rapid City - Short Hike. Nothing special. Something to do.
- Dinosaur Hill - Rapid City - Short Drive - Short look. Ditto on nothing special
- Sugar Shack - Deadwood - Food
- Alpine Inn - Hill City, SD
- Mt. Rushmore - (Keystone has some nice taffy)
If you are flying east:[*]Mitchell Corn Palace (almost as much of a tourist trap as wall drug)[*]Fly through the Badlands (east of Rapid/Wall Drug)[*]Missouri River (Chamberlain area) has some nice fishing / water sports / rentals available. Airstrip has courtesy car (or had last year at least)[*]Sioux Falls - The city has a place called the Falls. Worth maybe a landing?[*]Sioux Falls - Battleship (USS South Dakota). If you are a fan of the Navy, you'll get a laugh of what this actually is.[*]JL Beers - Sioux Falls - Burgers/Fries/Beer[*]Canton (South of Sioux Falls) . Sioux Valley Grille (Courtesy car recently available) -- Call ahead to airport
Wall Drug definitely the largest tourist trap ever.
If you are going to be in town (Rapid City) around the 4th of July, most places west of I-90 (runs North/South a bit once you hit Rapid going North) are banned from fireworks due to fires. Mt. Rushmore use to be a notable exception.
Hot Springs has Lake Angostura near. Can be a nice place for water sports as it's a larger body of water.
Otherwise, anywhere around the Deadwood/Nemo/Dalton lake area will be littered with Cabins/side-by-sides for rent if you want to enjoy the trees and hills. Following dirt roads and paths in 4 wheelers is a common SD west side past time.
Sturgis is pretty boring outside of August.