There are lots of accommodation options in the City Centre. I'm assuming, given that it's a stag do, you want something low key and low cost? If you are arriving by train, consider the Holiday Inn on the corner of Westmorland Road and St James' Boulevard. It's 3-4mins walk from the Central Station. Plenty of bars nearby and within reach of all the main nightlife areas in and around the town centre: Grey Street, Bigg Market, Quayside. Or if you prefer something more personal, there are apartments to rent in the complex adjacent (Central Lofts), as one of many examples. Travelodge Newcastle Central is on the Quayside itself, with a Premier Inn nearby. Lots of bars and eateries within 2-3mins walk and the most picturesque part of Newcastle. Also some better hotels in great locations on the Quayside, such as Malmaison or The Vermont.
If you choose to stay near the Central Station or Quayside you can't go wrong, as everything is within short walking distance. The centre of Newcastle is very compact, no need for public transport at all.
Home town but a number of years since I lived there, and I can't therefore recommend individual bars/clubs. You won't be short of choice!!