At BVI, Moore Aviation rents out 172Rs, Warrior IIIs, and a 172M to the general public. The only major restrictions I can recall off the top of my head are no flights beyond midnight or over the Appalachian Mountains, and the Great Lakes islands are off-limits (so no trips to Put-In-Bay). The fall semester at CCBC begins Monday, so weekdays will be fairly busy, but weekends are rather quiet. Not sure if ACES Aviation across the parking lot rents out their DA-20s and DA-40 to the general public.
Elsewhere, there is AirQuest Aviation at BTP, but I'm not sure if they rent out to the public. Haski Aviation at UCP has a couple Pipers. From what I hear, Pittsburgh Flight Training Center at AGC does not allow rentals without a CFI. There are flying clubs at BVI, PJC, AGC, and LBE if you want to go that route, and even a soaring club in Washington County at a grass strip.