Newcastle has so much culture and history, you could literary walk around in the city centre looking at the building and reading the little plaques on them - also look down at the plaques on the pavement.
There are loads of things to do outdoors, and you can just wander around looking at the view. Get yourself to the quayside now.
Newcastle likes nothing more than Drink, fun anf food. If you are in a party mood, get yourself down the Bigg Market - don't bother with a coat, even if it's freezing.