As others have said, a sort walk into york city and also a pleasent walk along the river to the Railway Museum, well worth a vist.
I only use the car, once there, to go to the local supermarket. Two local Wetherspoons provide Cask ale and meals at reasonable prices within a short walk. If you don't like walking, get on your bike, there are loads of cycle tracks along both sides of the river and also free fishing, when in season, within the city walls along the river Ouse. If you have a dog, again some very nice walks along the river when NOT in FLOOD, which is the only down side of this site.
Oh, forgot, you have to book realy early to get in, so popular.