This picks up a few more good places:
http://www.guardian.co.uk/travel/2009/nov/24/york-10-best-budget-eats
Other favourites:
(what it says, plus cheese)
http://www.yorkbeerandwineshop.co.uk
(Traffic free 5 mile ride out on a weekend morning for £2.99 breakfast! Good Sunday carvery too)
http://blacksmithsarmsnaburn.co.uk/
(One for the summer: SB is walking distance)
http://www.yorkcarboot.com/event dates.html
http://www.guardian.co.uk/travel/2009/nov/24/york-10-best-budget-eats
Other favourites:
(what it says, plus cheese)
http://www.yorkbeerandwineshop.co.uk
(Traffic free 5 mile ride out on a weekend morning for £2.99 breakfast! Good Sunday carvery too)
http://blacksmithsarmsnaburn.co.uk/
(One for the summer: SB is walking distance)
http://www.yorkcarboot.com/event dates.html

. If there isn't stuff you want, then there's stuff nearby back in Leeds and again York's rather spoiled on the transport links and the countryside around it if you do want to cycle. It depends on your philosophy of what living in a place is and really one can write a ridiculously long list of places to explore and so on but the person has to explore them themselves, a bit like what a guy said to me in Long Marston once when I was having a chat with him about bikes.