While I don't recommend carrying a mountain bike up the Limerock Trail as there isn't a lot of good places to ride up that way, and it's a long 4½  miles hauling over a few waterfalls and cliff edges, it can be done. Better just done walking, and enjoying the scenery.

Falls along Canaan Loop Road running into the Red Run.

Heading out of the Red Run hollow up to Canaan Mountain.