Beaver Creek Valley State Park has been mentioned more than once and its location is relatively central to the northern midwest. There are three primitive group sites, two handle up to 15 people, the other can handle 60 and they appear to be currently available the last weekend of October (Oct 26-28). Cost is $50 per night (plus some small fee to the reservation service, I think.
1) One night or two?
2) Are we willing all pitch in to share the cost?
3) Who can commit?
If we end up doing two nights I think it'd be fairest to divide up the cost of each night separately so that folks staying only one night are not paying for something they did not use.