How about a place like this?
http://www.gastateparks.org/info/amicalola/
North side of Atlanta, but not too far if done on a weekend. There are picnic areas, but they are first come/first serve basis unless rented for the day. rentals run about $30, which is no big deal, just have to reserve ahead of time.
The above link does provide links to other State Parks, ya'll look around and come up with something that is agreeable to as many as possible and we will make this happen.
Cheers!