We were there last year, arriving just before Mid-May. We stayed at Fishing Bridge Campground inside park. We prefer to stay in park when we visit, and it's centrally located. Plus it's the only one with hookups as far as I know (at least at that time of year), which we must have.
The Fishing Bridge campground was still opening different sections, so getting a reservation in mid-May should still be available. In summer the park gets too crowded for our taste.
There's a lot to see near Yellowstone, but the park itself is incredible if you like nature and wildlife. I could easily spend a full week there every year.
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