Last fall, I road tripped out and met up with a friend from the mid-west in Driggs. We just did day rides, but I would second LTrain's comments.
Although, this east coaster never expected all the wheat fields in the valley!
My buddy picked up this book, try to get a copy for some local knowledge:
Tetons: Looking East, from west of Driggs
In some places, you have to mindful of wilderness areas. This area was SE of Jackson (I would have to look up the name) and was more of a bunch of horse trails.
That pine bettle is doing a number.
We were out there in early September:
I would stop in Jackson. There are trails that lead right out of town, you can loop around or/over the Snow King (?) sky area and hook up with a bike trail. There is also a some fun trails on the pass between Jackson and Driggs.