The gravel riding is superb. There's all kinds of backcountry routes from Ashton down through Blackfoot and beyond to explore. Bone out and around the back of Taylor Mtn is a popular one.
For road, there's a decent amount of good routes. Dave's Bike Shop does Monday evening rides and Bill's Bike And Run does Wednesday evenings after closing.
For trails, the Kelly Canyon area starts at about 30 minutes from town and has a good selection of routes. Space Cruz is the most popular, and the general Buckskin Morgan and Fish Creek areas out there have well used trails. I generally prefer heading down to Pocatello for my longer rides as I like the terrain and options around Scout Mtn and Slate Mtn a touch better but that's just me. The Snake River Mountain Bike Club is riding on Thursday evenings until it gets dark early, then we do night rides until the snow sets in or it. Times and locations are posted on the club Facebook page, usually on Tuesday. Grand Targhee and Teton Pass are reasonably close, too.
If you don't have bear spray, buy some. A club member was surrounded by wolves while hiking with her dogs on Sidewinder trail last week and emptied her spray driving them away. I've seen bear and probable wolf tracks on rides within the last month or so.
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