I don't want to stay outside the park and drive all that distance every morning and evening,
Absolutely. I've stayed at the Old Faithful Inn as well as cabins in YNP (forget where, it was many moons ago on my honeymoon and oh ya, we broke a bed!) and I've stayed in many nicer places elsewhere BUT would stay in the park again. Comfort is somewhat secondary to location. It's amazing to walk out the front door to go to the geyser and have to stop because there's a buffalo in your way. A hotel in a border town is just that-a hotel. A property in the park boundaries is a very different experience.