You should contact the Park directly. From experience, I can tell you that the month of June is usually uncrowded. It's a large park, so you should have no trouble finding a great campsite.
Go online to Reserve America and book the party Pavillion down past site 258 on the lake near Juniper Island.
Depends on how many people you're sleeping per tent. How many sites you want etc. We had 12 people spread between 4 sites.
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