As far as I Know there are some student flats still north of the botanical garden, in the Baldwin Street area. But, and this is my opinion only, you have to be extremely careful with where you go there as the hill takes at lot of the sun away and there are some places which don't get any sun in winter at all. But having said that, you will find these places more or less throughout Dunedin, because it is so hilly.
We lived in St.Clair ("border' of) for a year and the house was freezing cold in winter, as the lounge/ kitchen area had about two to three hours of sun every say during the winter months. Would we have been on the opposite side of the road, it would have been different.....
I guess that you will find people who love where they are in every part of the town, it all depends on what your expectations are.
As mentioned before, a friend of mine said that Maori Hill is one of the coldest places, because of some winds, as far as I remember..., but it is definitely one of the more pricey areas and has a good reputation, as far as my knowledge goes.
St.Clair, St.Kilda and Andersons Bay are definitely further out, but not inaccessible.
If you try to research the areas beforehand by looking at Trademe, for example and then, when you're actually in Dunedin, try to go to different areas at different times of the day, that should give you a pretty good impression, I think?!