At Spearfish on the north side of Black Hills, take spearfish canyon and go down thru Lead and Deadwood, then you can go south further and hit Hill City and then south to Custer.
Just after dropping south from Lead, take the smaller Highway which goes thru Nemo as it is not traveled as much and is pretty neat. You can get back on 385 later and head into Hill City
You may want to stop and view Crazyhorse Monument between Hill City and Custer. It is a work in progress.
Then there's Hot Springs and they have a historic natural hot spring/swimming pool.
There's also Wind Cave National Park, and other various caves in the Black Hills.
You have to do the Needles Highway.
Here is the map I like of the Black Hills. The Custer State Park loop is toward the bottom and the circular route in Red which circles around Custer State Park also includes the Needles Hwy on toward the upper left and Iron Horse Hwy toward the upper right. Iron horse has some Cool views of Mt Rushmore.
http://blackhillsattraction.com/black-hills-map/