If you want to actually stay/camp in the park...you need to reserve a spot WAY in advance. Most of the places near all of the entrances book fast too!! AMAZING place to visit, BUT be prepared for loooooong lines (in your vehicle) and spending a ton of time driving to what you want to see! The park is HUGE

Definitely go to Firehole River and swim if it’s open (been closed due to COVID, but can also be closed if the water levels are too high). Lots of fun. Lived 20 minutes from it when a kid. Still have fond memories of it 40+ years later.

https://youtu.be/PgvJC7adqC8

Another cool place outside of Yellowstone is Virginia City and Nevada City, Montana. It’s about 1-½ hours out of West Yellowstone but is a fun place to check out for the day.

http://virginia city.com

Also, if you can’t stay in the park because there are no reservations, check out Island Park, ID. 20 minutes outside of West Yellowstone. Lots of vrbo’s. Henry’s Lake is a pretty area with homes to rent. Can get tubes and float down the Buffalo River or the Henry’s Fork.

We decidedto visit early June too. By Jan 4 none of the campgrounds had avail space. Some have first come but they say they're generally booked before 9am each morning. Yellowstone and Grand Tetons both allow booking 1 year in advance. Good luck to you.