Anyone have any suggestions for things to see and do with a 2 year old near FairPlay?
Fairplay's a small, laid-back community, so I think your 2 year old would be welcome most anywhere. South Park City, the restored mining town/museum is one of Fairplay's musts; while your 2 year old might not be much interested in some of the displays, he or she gets in free and could certainly toddle around with you and enjoy seeing wagons, a train car, etc.
I don't know what your travel dates are, but there will be several free concerts at the Fairplay Beach this summer--TGIFairplay. There's a fair and rodeo coming up as well. southparkchamber.com/calendar/calendar.html
There's a library in Fairplay which I would imagine would have a children's section if you need some quiet time.
Hiking was always a favorite activity with our little ones. They could walk a while and explore, looking for treasures like pine cones and bugs, then climb in to the backpack carrier for a ride. And of course having a few scenic drives planned for naptime usually works out well.