Of course the time will depend on what you want to see. But the valley and mountains are so different that fall is going on somewhere nearby from September through late October. I would check the Tetons website and Jackson CoC (Chamber of Commerce, not circle of confusion).
A couple of spots I like to visit are the old barnes north of Jackson and east of the airport. The other is a highway overlook north of the airport on the west side of the road. It is accross from some houses. Nice spot to see the mountains reflected in usually calm water.
Regardless of when you go, Anthony's, Bubba's and the Pearle Street Bagel are good places to eat. And there are several others too.