I went to the University & lived in Roath - nice big houses there. Also have lots of family living around Cardiff. I loved living in Cardiff & wouldn't hesitate to move back (although that is unlikely due to OHs work). Living in Roath was quite convenient - I was able to walk to most of the places I wanted to go to.
The uni is more towards the city centre - the buildings are fairly spread out but I would say that they are mainly within 15 mins walk of the city centre.
The buses are pretty good on the main routes into the city centre. Several serve the uni.
I don't really know that much about primary schools there but if you googled you would probably find out the websites & get some idea of ratings etc. I have seen several nice ones.
Highschools are also pretty good in general as well.
What I liked about Cardiff is the amount of green space. Roath park is lovely.
I would probably avoid living in the more studenty areas of Roath & Cathays - they aren't too bad areas but parking was a bit of a nightmare & there is the problem of them being a bit like ghost towns during the holidays.
I like Thornhill, Llanishen, Rhiwbini, Pantmawr, lovely houses in Cyncoed, Roath is nice.
If you want to look at bus routes the cardiff bus website is quite useful. Unfortunately I don't have it any more but it was easy to search for.