A trip to Durham by train, shopping in the city centre or the Metro Centre, a trip to Alnwick Castle, a visit to the Laing Gallery, maybe Gibside, food in the Bigg Market but only by day unless you like cattle markets, the Sunday quayside market, maybe a show at the Theatre Royal, the Baltic Gallery. That should do it!
If you do go to Durham, be sure to sit on the left hand side as you look towards the engine. You will know why when you look out as you arrive! If you want to scare yourself, go to the Weigh House in Grainger Market! They weigh you, just as they do the market goods, then issue a docket!
See something at the Baltic then walk down to the pitcher and piano for a cocktail (just for the nice view). Then walk up to have a drink down the ouseburn. The Tyne bar is particular good. Have lunch at Ernest (the flat breads are good) Have dinner at nudos on Low Friar St (Japanese cheapish)
If you do Durham, take some flats with you, or you're likely to see more of The University hospital of North Durham than you planned.
It's changed since I lived there, but Fish's Quayside suggestions are good. You can't go wrong with finding decent bars or places to eat, down there. You might still want to stick with the sensible shoes, though