Don't want to overstate the obvious, but you'll be just south of Grand Tetons and Yellowstone. If you haven't been, you must go, esp on a bike.
Just north of Jackson, look for the Scenic Loop Drive leaving from Moose Junction. I think it is paved, but nevertheless beautiful.
I think there are a couple of fire roads you can get well into the Tetons on, and will miss lots of other tourists in their Winnebagos. Wish I knew the numbers, but I saw them on a map at the visitors center.
Get on it and ride, you can't go wrong. (Watch your fuel though!)
Steve in AZ...
Time is the greatest teacher...but it kills all the students!