The Town Wall - decent upmarket 'boozer' -
http://www.thetownwall.com/
The Forth - another decent 'booozer' opposite The Town Wall and owned by the same people who own The Adelphi in Leeds -
http://www.theforthnewcastle.co.uk/
Tokyo - decent rooftop place 2 mnins walk from The Forth -
http://www.tokyonewcastle.co.uk/
The other ones I like will not let you in I reckon + they are more a chew on to get to.
Then if you want to get more lairy head across to Collingwood Street (20 yards from Tokyo) - a bit 'Geordie Shore' but busy and an 'experience' for Southerners....
Vodka Revolution. Standard.
Madam Koo's - big rammed mainstream place (but full of 'birds') -
http://www.madamekoo.co.uk/
Babby Lynch - Saudi Sportswashing Machine's answer to Oporto -
http://www.babylynch.com/
Florita's - another rammed mainstream place (but full of 'birds') -
http://www.floritasbar.com/
Personally I'm not a fan of Collingwood Street but loads of people love it and it will be full of geordies... Steer clear of the Bigg Market, The Gate and the Quayside - mainly horrendously chavvy....
If you get sick of Geordie Shoresville you could try The Cut after 12 (where I go if I'm not going proper clubbing) - little club just round the corner that plays random beats and decent 80's and that -
http://www.whatisthecut.com/
Alternatively there is Grey Street - they've got a Brown's, a Living Room, Bar Luga etc
Bear in mind that nearly everything shuts by 1am except Madfame Koo's, Baby Lynch, The Cut, Digital and Aspers casino....