Depends when you are going; many of the CGs (including SPs) around here close down or offer limited services by November. Closest choice by far is Illinois Beach State Park. Decent enough, and I believe they have some sites with more than just electric hookups. Probably 15-20 miles from the base.
Our old standbys when we lived in that area are Chain o' Lakes SP and Bong SRA (all 3 of these are mentioned in the link 2gypsies provided.) We like both of those CGs better, and if you choose Chain o' Lakes, I'd recommend the Fox Den CG there, over Honeysuckle Hollow, as sites are bigger and the bathhouse newer. Both of these CGs will be roughly 25-30 miles (perhaps a bit more) from the base. Electric hookups in many sites in both these parks. Bong, like all Wisconsin state parks, has an entry fee in addition to camping fees (but we never had a problem paying it - loved the park.) Illinois, last we knew, does not charge such an entry fee, but you may notice some difference. :)
It's pretty urban around there, so you won't find anything closer to the base.