Newcastle is a pretty small & compact city , by anyones standards. Once you get into the town centre, everything - & I mean everything - is within staggering distance. The Quayside is pretty good - lots of bars & clubs wherever you go - but be prepared for an early start, as UK licencing laws can still be a problem - Pubs usually shut at 11 PM , clubs 2 or 3 , but everyone is usually out & about by 7/7.30.
If you are not sure where to go , head for the Bigg Market - just listen for the noise & follow it !. Its only 10 mins from St James park & could be described as the centtre of Newcastle Night Life ( although this is debateable ). Depending upon your tastes - be they mainstream or other ( remember that there about about 100,000 students in newcastle ) , there are niches for everyone.
If you have time , check out the cynical , but well informed website :
http://www.theburglarsdog.co.uk/
its independent , but worth reading - contains maps also. For the uninitiated , the Toon on a Saturday night can be a revelation - prepare to queue for some of the more trendy pubs & bars. My own personal recs. would be :
The Cooperage - Quayside
The Bridge - At the end of the Brodge ( funnily enough )
The Trent house - Next to the gound.
Also , If you get time , Please try to make time to get uup to the Roman wall - magnificent & desolate - & only an hours drive from Newcastle . The Northumberland coastline , north of Newcastle is also wonderful & mostly unspoilt.
have a good time!