I've stayed in West Yellowstone every single year since 1974 for at least a week (snowmobiling), and have stayed at many of the properties in town. One of your bigger issues is going to be availability, as you have found the rates are WAY higher in the summer than they are in the winter when we are there sledding. We now go to VRBO and rent a house or condo, but we are there for a week.
I can tell you the properties on the north side of town are older, the ones on the south side are much newer. The town did a land swap with the forest service a few years back, and all of the new stuff is on the south side. That said, you can still find good ones in the old section. We have stayed at most every one of the Best Westerns (there are like four or five) and of course the Stagecoach Inn is a classic. There is a newer Holiday Inn on the south edge, fairly new, always been good as well.
One post mentioned going to Gardner instead at the north entrance, good advice. Stayed there too. And Cooke City. And Red Lodge (Bogart's Pizza is worth the stop). I could go on and on, but we are usually there in the winter, not nearly as often in the summer. Too many people.
If possible drop over to Island Park (head west out of town on U.S. 20) and go down to Mesa Falls, on the south west side of the park, to get away from the crowds. One of my faves is Cave Falls, far south west corner, few ever go there. Here is a photo from the winter of Cave Falls, and one of the falls from inside the cave. Have fun!
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