Stylish traditional restaurant in York?

[PaxUniversalis]

Can anyone recommend a good restaurant in the historic centre of York? The two couples (relatives from abroad) who will be travelling with DH and me are in their early 70s and they like going to stylish, traditional restaurants. Nothing too casual or noisy so no loud music. Tablecloths rather than bare tables or 'canteen-style' interior (as they call it). Traditional and a bit upmarket but not the most expensive places in town either. Ideally local or regional food. Efficient service by knowledgeable staff. Thanks.

Maybe the star in the city, lovely building though the food isn't as food as some. My favourite is cafe no 8 on hillygate. No tablecloths but v good food.

Gillygate!

NorthernLurker - that looks great, thank you very much. I'd like to try it. I haven't been back to York since 1987 (!) so it's a bit hit and miss without some local advice, especially when travelling with older relatives who haven't been there either. Thanks again.