Indepdendent's generally the best night out on a Monday, though it went downhill last year when they decided to stop serving doubles and limit the amount of drinks you bought at once. Arizona maybe worth a go on Monday if you like cheesy music, very cheap too from what I remember. Think this has changed recently though, so hopefully it'll be back to it's best next year. Everyone then seemed to decide to go to Privilege on Wednesday (cheap, but generally cramped with poor music, taking about 20 minutes to get served at the bar). The Indigo Rooms has recently opened, which is a nice bar and is apparently decent on Thursday nights, though most people go to Passion that night. Passion's good if you like rock music, and drinks are £2. Beer's generally crap, though. Cheapest pubs will be Porterfields, The Londonderry (tends to be full of old people, though), Greens and Yates'. Establishment is well priced too, and has a free jukebox. Ttonic also tends do £1 Jagerbombs most nights, too.
Avoid The Cooper Rose - it is nice, but despite being a Wetherspoon's, is more expensive than the other two. The Lambton Worm is just down the road, and also a Wetherspoon's, but cheaper. It's also next to Greens, Establishment, and Revolution (expensive, but get a Privilege card and it'll help - you'll get nice and drunk there).
You'll stop going to North Shore after freshers, too. It's good while everyone's there for a couple of weeks, but nobody goes after. You'll have a much better night in town/Newcastle. I don't know Newcastle as well, but you'll get some £2 trebles there in Gotham Town, directly opposite the train station. Generally a good night out though.