York is a really easy city to explore on foot.
Most of the best attractions are covered above, but I’d add The Dig and second the Castle Museum.
If you stay outside York use the Park and Ride. It’ll save you a load of hassle parking.
Your better half may appreciate a trip to the Designer Outlet (can’t see the attraction myself)
Further afield:
Helmsley is a nice market town and you can visit Duncombe Park.
Castle Howard is nice.
Newby Hall near Ripon is good.
Scarborough, Whitby, Filey and Bridlington are about an hour away. Whitby for F&C. Filey for beaches. Scarborough and Brid for beaches and amusement arcades (2p droppers keep my wife and daughter amused).
Food:
Walmgate/Fossgate have a good run of decent restaurants.
Barbakan – Polish – Would recommend booking – great breakfast & desserts
Meltons Two – British
Khao San Road – Thai, although we prefer The Old Siam on Micklegate
Loch Fyne – Seafood
Mumbai Lounge – Indian
Rustique is a very good french restaurant.
If you really like Indian then Coconut Lagoon on Clarence Street is very good. Try the Dhosa.
There are too many good pubs to mention all our favourites, but the Ossett Brewery owned The Hop has a good selection of beers (and wood fired pizza), and the House Of Trembling Madness is worth a visit.