Echo the above, it depends where you are in Newcastle too, or if indeed you end up in Gateshead!
Chopwell is surprisingly good given there are only 2 (?) official trails. Its so compact you can just follow your nose and find stuff. If you decide to head that way then you can see most trails on strava or I can send you a link to rides I’ve done round there.
Hamsterley is a trail centre. You can bomb round it quickly and short cut for a quick ride or extend it out onto the moors, look for the “secret” stuff and make a day of it. Again, I can send you some links to longer day rides. The shorter options are all signed.
Kielder could be miles away but is also good, more XC than hamsterley in my experience.
Other stuff I’d want a guide unless you are happy to follow a GPX. I could send you routes around Newcastle. Not very exciting but entertaining for a few hours in the evening. Probably all footpaths (I thought Plessey was?).
Interesting a few places mentioned above I don’t know about so I’m looking at maps now!