YES! I was there for work a few years back and there are indeed some great trails there. I forget the names though. The ones I rode were south of town, one on the east side of the main road near some reservoir (great high country ride after a lung busting climb) and the other was further south (I think, maybe called Dry Creek/Springs Trail) and had lots of fun twisty turns through aspens.
No one rides in Afton and the sports shop barely carries tubes so get a map, bring all your spare parts, and explore!