Up in the eastern panhandle, Apalachicola National Forest and Tate's Hell State Forest have a lot of interconnected roads that are not terribly challenging, but way out there. The Southeast Adventure Trail has mapped a route through (can't post links yet), plus a route from Carrabelle east across the state that is mostly unpaved. Getting the Motor Vehicle Use map from the USFS for either Apalachicola or Ocala NF will show you lots of options plus marked campsites. The Gaia app has the MVUM as an overlay, and shows campsites as well. It's getting close to hunting season, so you'll want to check what roads and areas are closed/restricted due to hunting season.
SW Ga (where I live) is primarily private land - some of the state property like WMAs has fun short-term exploration, but not a ton. There are a few longer dirt stretches in east GA (other side of the Okeefenokee), and some large Wildlife Management areas and National Wildlife Areas to explore.