Breckenridge is just a short and beautiful 30 minute drive from Fairplay over Hoosier Pass. There are a ton of great activities to do both in the town and at the ski resort. There is a free gondola that goes to the base of the ski resort from town where you can take a scenic chairlift ride, mountain bike, ride the alpine slide, mini golf, and more. The town of Breckenridge has great shops and restaurants as well!
There are a few great hiking options in the Alma/Fairplay area. Provided below is a link with a trailforks collection of trails in the area with varying degrees of difficulty. Feel free to branch out to the Breckenridge, Buena Vista, and Leadville areas as well if you have some extra time and want to explore!