I live here, I can say the students tend to be situated around the uni which is right by the city centre.
If you need to travel around we've got the train and bus station in the city centre, megabus comes here and we've got first bus which links you to cornwall. A good thing is they've now introduced a skipper ticket (could be wrong on the name) which acts as a day rider but will let you use any bus in the city (Citybus, first bus, target travel)
We've got ferries which take you to mt edgcumbe (also in cornwall) and the torpoint ferry which takes you to torpoint across the tamar.
The uni itself is in one big clump in the north hill area. At the base of said hill is Drakes Circus which is the mall. Surrounding that is the city centre. There is a long stretch known as Royal Parade where all the buses travel to and stop to swap drivers. Leading on from there is union street with numerous clubs and as you go further along towards the area of devonport there is a Lidl and Aldi.
Within the city centre we frequently have farmer and continental markets and a christmas fayre.
Things to do: Ice skating, go see a band in the pavillions, go to reel (a small cinema, smaller screens but cheap as chips), go up to the hoe - crazy golf, bowls, go to the barbican leisure centre where there is bowling, an arcade and cinema. Or go to central park which is right by the life centre where you can go swimming, play numerous sports. Or wait til the summer and the outdoor tinside pool opens.
For yer grub we also have a big sainsburys in town, iceland and a tesco metro.
In the other direction, at the top of north hill you find mutley plain which is a mix charity shops, take aways, convenience stores(2 co-ops, a new morrisons, tesco, sainsburys) , barbers/hair dressers and a few foreign shops (2 polish, 1 east european, 1 asian) and several pubs which have dwindled recently.
Hope my half asleep ramblings are of use.