You need to go down to Mount Rushmore then take Iron Mountain south. You will love it with the switchbacks and pigtails.
Enjoy the Black Hills - plenty to do as many mentioned in their posts here. I would add to this comment that Iron Mountain Road (highway 16A) is a great ride as explained - do this route as stated and then go back towards Mt. Rushmore on Iron Mountain Road - you will see Mount Rushmore framed by some of the tunnels when you do this reverse trip!
I lived out in Rapid City for 4 years when in college (1973 -1977). My wife's family lives out there and we go there 4-5 times a year! Never get tired of it....some of my favorites are (sorry if it repeats some from previous posts):''
* Rapid City to Sturgis take Nemo Road to Vanocker Canyon - great ride (or reverse)
* Spearfish Canyon
* Deadwood - interesting town, also can go to Lead, SD adjacent to Deadwood if you're interested in a "mining" town - several free sites to see
* Devils Tower in Wyoming (you can do this by going to Belle Fourche then towards Wyoming (hwy 34/24) to Hulett then Devils Tower back through Wyoming (hwy385/85) to Black Hills via Newcaste, Custer, Needles Highway, etc. If you have time there is a free museum in Belle Fourche...Tri State Museum
* Lots of other places like Custer State Park (I worked there one summer while in college - tour guide)
There is a free road guide map at just about any stop - tear one (or two) off of the pad at these places - it's a good view of the Black Hills, tour sites, roads, etc.
If you have any specific questions, just PM me....
I wish you a great time and safe travels! :thumbup: