What about landing in Billings, MT? This would allow you to enter the park via the Beartooth Pass. I grew up in Red Lodge, which is just at the base of the pass, and it's breathtaking. There's a tiny gas station/ souviner shop at the top called Top of the World Store, and it really looks as if you were on top of the world!!!
I believe the drive from Billings to Yellowstone would be around 6 hours. Someone correct me if I'm wrong.
You won't be disappointed if you should choose this route!!