The station hotel is lovely, at work we do our training conferences there, its so old fashioned, love it. The Hilton is good too, just over the river in Gateshead and there are several Premier Inns, you need to check online.
The shops are great in Newcastle and the Metro centre but to go to the Metro centre you need to get a bus from Eldon Square takes about 15 mins, or an mainline train from central station as there is no metro station at Metro centre, you can get a metro train to Gatehead then a bus to the shops. So complicated.
The theatre royal in Grey street is fabulous, always something good on, I used to go regularly when I was younger, do have a walk down to Bigg Market by grey street and see the culture (maybe not on a Friday night though). There are so many bars and pubs, you could spend weeks and not get tired of Newcastle.
As someone else says, you can get a train to Alnmouth, or Morpeth and be in reach of lovely countryside or keep on the train to Edinburgh. You are making me envious just thinking about our lovely county.