You can now book reservations for campgrounds within the ANF. In order from the closest to GeoWoodstock, these are...
Buckaloons is a quiet campground within minutes of the Warren County Fairgrounds.
Farnsworth Cabin is a very interesting CCC-built cabin which sleeps eight. The building was just restored and looks really great from the photos. This is a historical cabin with geocaches and waymarks just outside your door.
Dewdrop (no electricity) is located near the very scenic Allegheny Reservoir.
Kiasutha is in the Kinzua Dam area and has space for motorhomes.
Redbridge also offers space for motorhomes.
These are the five closest sites to GeoWoodstock. If you are looking to move to more than one area while visiting, this link will send you to all the camping spots on ANF or Army Corps lands within the area.