Larry.. Cooke City is closer, I was going to suggest that too..
But in favor of Gardiner
- Gardiner has Park's Fly shop (the shop in Cooke City closed - at least the ast time I was there)
- You can get to other parts of the park easier - if those NE rivers are (and they can be) very crowded that time of year, and options to go east or south
- More choice of places to stay