It's my impression that when the students venture south in Leamington, they don't go very far south.
So there are a lot of students in the area south of the river but north of the canal around Kelsey's and then spreading further south of the canal to the roads between Tachbrook Rd and Clemens/Brunswick St and off them (Charlotte St, Claremont Rd, Aylesford St, etc.) which are all within about 10 minutes walk/stagger from Kelsey's and near to the bus route.
This is a good area for the buses as it's near the start of the main bus route so you are more likely to not just be able to get on the bus but also get a seat!
I would say this is a fairly typical student area. It has a bit more of an uncared-for feeling than some parts of the North, in the way that student areas often do, but it isn't dangerous for students because there are so many of them living around there that there will always be other students walking home in your direction.
Generally, the North is nicer and more convenient for entertainment and the journey to campus is a bit shorter (if you can actually get on the bus). The South is less nice, but usually cheaper, more convenient for the big supermarkets and you are more likely to be able to get on the bus to campus.
Ideally, you want to be within about a 10 minute walk of a bus stop on the main route to campus as the bus can take well over the 30-40 minutes they claim due to traffic. You have to also factor in the possibility of having to wait around for a bus with space on it at the beginning and end of the day.
The student area in Coventry (around Earlsdon) is more convenient, but I think that Leam is the more popular and social area now, especially for UK students, and it would be a long way to travel if all your friends were living in Leamington.