I just searched and didn't find much closer than 25 miles
2 thoughts-- It's just for the weekend- WHY do you need full hookups?
Nearby state parks will have electric and you can fill your tank
when you get there.
Michigan state parks have pretty good rest rooms IMO.
They don't allow alcohol but if you're discrete and don't sit around
with a beer can in your hand- no one will know or care.
Michigan parks tend to fill up on weekends so get your reservation
in NOW. It might not be too late!
My 2¢