Last summer, I enjoyed taking an American (that I know from Circvs Maximvs) to a local restaurant: 
http://www.thebroadchare.co.uk/proper-food/
He's quite a foodie, and said that it was the best meal he had on his vacation here (he only spent one night in Newcastle, and the rest up in Scotland or down around London).
Here's the menu, for anyone interested in what "British" food might look like:
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Bar food 
Lindisfarne Oysters
 £2.00 
Cauliflower Fritters - Curry Mayonnaise
 £3.20 
Deep-fried Monkfish Cheeks
 £3.50 
Crispy Pigs' Ears
 £2.80 
Handraised Pork Pie
 £3.50 
Scotch Egg
 £3.50 
Middlewhite Pork Crackling and Bramley Apple Sauce
 £2.80 
Small plates 
Chicory Salad, Pears, Blue Cheese & Walnuts
 £6.40 
Pork and Pistachio Terrine, Pickles and Toast
 £7.60 
Smoked Mackerel Pate- Beetroot & Apple Chutney
 £7.20 
Cauliflower Soup with Montgomery’s Cheddar
 £5.50 
Warm Onion Tart, Fried Duck Egg & Wild Mushrooms
 £7.40 
Potted Shrimps and Hot Toast
 £7.80 
Large plates 
Spicy Black Pudding, Smoked Haddock and Mustard
 £14.50 
Lentil & Root Vegetable Masala
 £10.00 
Rare-Breed Pork Belly, Garden Brassica & Scrumpy
 £15.00 
Grilled Calves Liver, Bacon & Onions
 £15.00 
Rib Eye Steak, Onion Rings & Watercress
 £19.50 
Mutton Masala
 £13.00 
Ground Rib Steak Burger with Northumberland Cheese
 £10.50 
On toast 
Pig’s Trotters and Montgomery’s Cheddar
 £7.20 
Fried Mushrooms with Mustard Butter
 £6.00 
Haggis, Fried Duck Egg & HP Sauce
 £7.60 
Local Crab
 £7.90 
Sides 
Hot Pease Pudding
 £2.00 
Steamed Greens
 £2.60 
Mixed Salad
 £3.00 
Onion Rings
 £2.50 
Pickled Red Cabbage
 £2.00 
Mash
 £2.40 
Handcut Chips
 £2.40 
Desserts 
Warm Honey & Spice Cake-Cider Sauce
 £5.50 
Rhubarb Crumble with Custard
 £5.50 
Toffee Apple & Pecan Nut Sundae
 £6.00 
Chocolate Stout Mousse with Ginger Snaps
 £5.50 
Ices; Vanilla, Earl Grey, Strawberry
 £5.00 
Cheeses 
Adrahan, County Cork
 £4.20 
Montgomery's Cheddar - Somerset
 £4.20 
Mrs. Kirkhams - Lancashire
 £4.20 
Stichelton - Nottinghamshire
 £4.20 
Selection of Three
 £8.50
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(Obviously, other British foods are available)