hit the park for a day or two. Advantages would be availability of things like ATV/Side by side rentals and trails, water skiing/jet skiing, lots of vrbo/airbnb lodging, etc.
If the main point is to be in the park all day, definitely try to get lodge/campsite in the park or West Yellowstone as an alternative. Any of them are going to fill up quick though, so make a decision and go for it.