Whether you are an experienced climber who chooses their own routes or a newbie who needs a guide, the Black Hills has many options for rock climbing.
Luckily, Hot Springs is near one of the best places to climb in the Black Hills: Custer State Park has renowned climbing in its Sylvan Lake and Needles areas.
You can take a guided climb with Sylvan Rocks Climbing School and Guide Service. The climbs meet in the town of Custer (about 40 minutes from Hot Springs), then travels to Custer State Park. They have options for 4-8 hour, all-equipment-included expeditions for new climbers, groups, and families, or multi-day options for experienced climbers.
Another option for guided climbs is Buck Wild Climbing.
Venture farther north in the Black Hills and you can climb Spearfish Canyon, Mount Rushmore (the back side), and Devils Tower.
For more climbing information and route recommendations, Black Hills Climbers is an excellent local resource.