Why not plan a loop around Lake Michigan? We did a similar trip years ago and it is still one of our kids favorites!
Start at D H Day campground near Sleeping Bear Dunes National Lake Shore. Head up to Petkosky for a few days. There is a lake front state park there. You can then camp near Mackinaw Island. You can take the bridge to the UP and work your way over to Door County, WI. Peninsular State Park in Door County is very nice. On your way back to NJ you can spend time visiting Chicago and stay in a state park, Indiana Dunes near Gary, ID.
You are wise to plan and book in advance. I know that D H Day and Peninsular campgrounds are very popular.