Obvs there's the free courtesy bus you can use - that was introduced while I was living in St. Mary's in 2010, so I'd bought a bus pass.
Stagecoach Uniriders are £250 for the year:
https://www.stagecoachbus.com/newcastle-unirider.aspxI did start using the courtesy bus occasionally once it started, but always got the bus home from uni after as they only run 2 journeys home so they rarely fit with when I wanted to leave.
In terms of buses - 36 and 63 both run every 15 mins. Both drop off at St James' Park opposite the Business School and 10 mins walk from main campus. 36 then goes round down by the train station and the 63 goes straight through the city centre dropping off by Eldon/Square Monument.
The 15/15A runs every 30 mins. The half past bus usually gets you to class on time. And this drops off by medical/dental school and then on St Thomas Street right next to campus.
The half past bus had a habit of being late, so although I don't think it ever actually made me late, I'd have those mornings of debate over whether I should get the 36/63 and walk in or keep waiting. By which point it'd be too late to get the 36/63 or I'd be late for class.... which is why I started using the courtesy bus a little just for that guarantee. But I only had 3 days a week where my classes started when the courtesy bus was running!
Lots of people get/bring bikes, and I've even known people walk it. Taxis used to cost £4-5. I don't think that should have changed much!
If you plan to use public buses getting the pass could work out cheapest, even if you use the courtesy bus in the morning. I think a single fare was something like £1.60 ish so you don't need to travel often to get your moneys worth. And as I pointed out the courtesy bus might not fit with your timetable, and there's always weekends when you might want buses too.
As for living there - I liked St Mary's. It's quiet but that doesn't mean it's not sociable. There's still flat parties and the social areas in the main building. There's also a big Morrison's about 10 mins walk around the corner which makes shopping nice and convenient!