Another place I'd recommend in York is Monty's Grill. I also mainly does steak and seafood, but it's not as up-market as Harvilles. I haven't been at the weekend, but apparently their Sunday lunch is particularly good.

St Peter's Grove, York.
www.montysgrill.co.uk

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This is a tiny shop (you probably couldn't fit more than five people in there at once) in The Shambles that has an extensive menu of great sub-style sandwiches that all cost only £1. It's the perfect place to pick up lunch to eat in a park on a sunny day.

The Shambles, York

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