We just got back from Jackson two weeks ago. We stayed in Jackson because my husband had to attend two mornings of "meetings" The drive from the Village to Yellowstone was about an hour if you take out the stops we made along the way. We left the hotel at 6:00 and hit Old Faithful about 10:00 a.m. We made it back to Jackson at 6:00 - it was a very long day and we didn't get to see nearly enough. HOWEVER, I enjoyed our time in the Tetons much more than Yellowstone - mostly because the crowds were much smaller and I arranged for a professional photographer that's lived in the area for over 30 years to show us around; it was the best money we spent the entire trip. Scott McKinley showed us places most tourists dont get to and also taught us a great deal about the biology of both parks - he gave me some great photography tips as well. Here's a link to his website.
http://http://www.scottmckinleyproductions.com/
We saw a mother grizley and her cubs (thanks to Scott) a cow moose and her calf (several evenings the same place), hundreds of elk on Moose Wilson Rd (between the Village and a short cut to the main hwy to Yellowstone, bison, antelope, bald eagles, golden eagles and osprey to name a few. If you want to take landscape photography, this is the place to be - it's simply breathtaking!