I believe the only cg in Frankenmuth is a Jellystone, if that's your kind of thing. About 20 miles away, roughly a half hour drive, is a place called Covenant Hills. It's in the town of Otisville. It's a big campground with a lake, and a zipline, and some other amenities. Staff is nice, that the sites aren't too small. It's $35 per night for full hookups. It is a Christian camp, so no alcohol, and they have a dress code.
I've heard great things about Covenant Hills from my cousin who camps there often (she lives in nearby Columbiaville). She says that they don't push Methodist-ism on anyone (if that's a factor), but I didn't know about the alcohol. I suppose I'll have to turn down her next invitation.
We stayed at the Jellystone Frankenmuth on Weiss St just last month and were VERY impressed! Well kept, level sites, clean bathhouses, and across the street from Bronners! And less than a 5 min drive to the main Frankenmuth town! Would do it again in a heartbeat! They also give you a book of many coupons for the shops & restaurants there.