Newcastle is my favourite city in the UK; I absolutley love it there. Yes, you have the metro centre in Gateshead which is the biggest shopping centre in Europe and you won't cover it in a day, you have eldon square in the city centre plus the huge array of other shops there.
The Quayside is a great place to go and chill out, theres some nice restraunts on the cobbled road which leads down to the Quayside, I especially recommend Uno's; beutiful pizzas which are on offer during daytime of weekdays. There's also a mongolian restaurant.
Visit the Baltic flour mill on the Quayside, its a museum thats free and offers some good views of the tyne bridge on the viewing deck. Oh, and if you can, try stay the night and go out, bring a few mates up, brill nightlife! The cafe there is also awesome, proper nice organic stuff thats a bit costly but tastes delicious.