I'm not sure about camping, but if you're gonna be in that area, I would highly recommend heading 45 minutes south to the Appleton area. There is some amazing DG all over that town. The can't-miss courses would include Grignon Park (18) in Kaukauna, Telulah Park (18) in Appleton, and best of all, the simply gorgeous Plamann Park (27) in Appleton. It's easily in my top 10 of the nearly 200 courses I've played.
In Green Bay itself, I've only played the Triangle Sports Area course, which is a solid, fun round, but dude, if you can make it down to Appleton, don't pass up that opportunity. Wisconsin is full of great DG. And it's too bad you don't have more time, otherwise I'd recommend the 5-hour drive up to High Bridge, WI, which offers camping and no less than six 18-hole courses right on the same massive compound. There's nothing else like it. Have fun!