West Yellowstone for certain, and there were only a couple motels there at that time. I was four or five years old, first trip to Yellowstone with my parents and 2 year old brother, coming in via Rexburg, Idaho. I don't remember the motel name (though I'd have been well able to read the sign in 1965).
@Donald Qualls : funnily enough, Rexburg was one of the locations I chose for looking the 2017 Eclipse. But we finally stayed at Roberts, Idaho, no so far away