Definitely budget some time to go hiking/climbing in the Tetons, it will be time well spent. Garnet Canyon/Middle Teton, Amphitheatre Lake, Cascade Canyon and Paintbrush Canyon are all worth seeing. If you're really feeling strong, hiking up Paintbrush Canyon and down Cascade Canyon in one long day is a good challenge.

I would expect flights to and from Jackson Hole Airport to cost a bit more than flights to/from any nearby cities, you might want to check prices to Missoula, Bozeman, etc. if that matters to you.