Hi, We are from Iowa and go to yellowstone once in a while.
1. Hotels inside fill fast.
2. Outside hotels on the west and north side are not that far away. There are a few more tourist things to do at west side entrance.
3. It snows sometimes even in early June.
4. The distances are deceptive. IE: a 20 mile stretch of road may require 3 hours to cover. The traffic stops for animals and sightseers.
5. We stop at every sight with a parking lot.
6. We live in a low altitude state and it takes a couple of days to be able to hike at a reasonable pace, in the thin air. We plan for that now.
7. Read some guidebooks. The park does not change, so earlier editions of books are fine.
My must-see list
1. Old faithful and surroundings
2. Gibbon falls
3. Waterfall from several trials
4. Canyon

I love it there, as you may have suspected.