A big second to Chuck's recommendation for Door County, specifically Peninsula State Park. You can't do much better for hiking and biking, kayaking is good too as long as you're looking for open water (it's right on a bay) as opposed to river or stream. We've been going there every Labor Day for 10+ years and love it. You can still get a spot for a week in June but I wouldn't wait too long, no electric sites but still some tent/small RV. For a nice wooded site I'd suggest either Welcker's or South Nicolet Bay campgrounds. Both have easy access to the water and hiking & bike trails. Should be about a 7 hour drive from Fort Wayne depending on the time & traffic you run into around Chicago. Go for it, you won't be disappointed!
