We want to go to Bignor Roman Villa, Weald and Downland Open Air Museum, then return to Heathrow. We do not want to rent a car. Does anyone have recommendations about lodging and private car hire in the area? I think getting around by buses and trains would be very difficult.
I know the area fairly well and agree that seeing all those by public transport would be very difficult, just a terminology point to note, in the UK "car hire" means a "rental car" as you would call it. What I imagine you mean is a car and driver, sorry can't help you with that as I own a car and have never had to pay a driver, also I would rate Fisbourne Roman Villa over the Bignor one. I can only suggest that you get the Train to Chichester and try to find a car and driver online beforehand to take you to these places.