OP: I'm going to Newcastle, what can you recommend
Most posters: Drive out of Newcastle and visit elsewhere
There are a lot of things to do in Newcastle itself and in the immediate surrounds, although I do recommend getting a metro out to Tynemouth if you can. I would park the car and just use the metro. Some have already been mentioned but I will write down the things I have done and enjoyed over the years
The castle - this very rarely gets mentioned as worth a visit but it really is. When the railway was built they knocked down part of the castle to run the line through the middle of it. Fortunately public outrage stopped any further demolition.
Grey Street has lots of fine buildings and Grey's monument
Museums - Discovery museum, Great North Museum: Hancock, Life Science Centre
Shopping - Eldon Square the M & S in Newcastle has the best food department in any M & S I have visited
Tynemouth Market - Saturday and Sunday mornings. Don't drive. Get the metro. There isn't enough parking and they are quick to give out parking tickets (bitter experience). There is also Tynemouth Priory. Further up the coast is St Mary's island in Whitley Bay with a lighthouse that you can climb up.
Wander along the quayside
Underground tour in Victoria tunnel
Grainger market
Jesmond Dene - although it is at its best in late May/early June. William Armstrong (Cragside) landscaped it and it is an absolute jewel of an oasis in the middle of Jesmond
Visit the Angel of the North on the way up
Loads of places to eat. We particularly liked Saray Turkish Grill in Jesmond and Chaophraya in Eldon Square. We also have eaten at loads of other places and never had a bad meal
DD was a student in Newcastle then stayed on after graduating so we have visited a lot.