Yes! If you get a tourist map it'll show the different kind of rates - you can also park in the park and rides depending on times and stuff.
I've always parked in and around York when me and Sarah have gone and I never felt overly ripped off.
Andy, answer the man's question about parking. You parked last time didn't you?
http://www.york.gov.uk/transport/Parking/Car_parks/
It all looks dear :(
Milko: Yes, you both are. Haven't you booked your train ticket yet? Sheesh.