The Mason's Arms is a little way out of the city centre (not miles, but you wouldn't find it unless you were going there) and I have heard only good things about their sunday lunches.

In the city centre, there are two branches of Russell's carvery. They've been around for many years and are a local firm, but I don't recall ever having spoken to anyone who's been there - they can't be doing much wrong to have survived so long though.

The Royal York Hotel next to York railway station does an excellent Sunday lunch at a very reasonable price too. Open to non-residents.

If you have a car drive to the White Bear at Stillington about 15 minutes outside of York on the A19 north.

channel4.com/food/big-food-map/explore-map/

I can safely vouch for the Mason's Arm's food anytime, it is delicious and well worth a trip. It's only a 5 minute walk from the city centre, you could even walk round some of the walls to get to it and get off at Fishergte Postern.

Also, maybe try Lady Anne Middletons. We ate there last week for my birthday and it was lovely. It's a hotel but is open to non-residents and they have a really nice atmosphere and lovely gardens etc. £12.50 for a 3 course meal with bar prices very reasonable indeed. http://www.ladyannes.co.uk/

I went last weekend and ended up going to the guy fawkes inn, it was very nice, thank you all anyway