Hi Joe,
As an ex-resident, I can confirm that York's a bit hit and miss with food, some really nice places mixed in with some really poor tourist traps.
To be honest I'd be struggling to recommend a pub grub type establishment in town, however if you're prepared to travel 10 mins down the A64 towards Leeds, Ye Olde Sun Inn in Colton is fantastic.
City centre-wise, my recommendations would be:
Evil Eye, Stonegate - trendy cocktail bar place that does really good, super-authentic Thai food
El Piano, behind Stonegate - Vegan restaurant, top notch
Oscar's, Stonegate Yard - no-nonsense, good value stodge - huge burgers, steaks etc
Will ask a mate and post back if he recommends owt else.