Both times I went I drove from the East coast so I don't know much about flying there... I know you can also fly to Cody wyoming, It's definitely farther but might work out better. (If you are in Cody check out the night rodeo, it's a lot of fun)
If you're not planning on doing any serious hiking you don't need more then a day there. (OK, in August 2 days. There's so many people and so much traffic it can take an entire day just to drive across the park)
If you have a choice between Yellowstone and Glacier go to Glacier.