First off there are pockets of the North Side of the city that are very dodgy. Be careful around Parnell Street, top of O'Connell Street and streets East of O'Connell Street. I'm not going to diss the entire North Side - much of it outside the city centre is fine, but South side is much calmer, nicer and well, just better (well most of it!).
Which University? Trinity, UCD, TUD, DCU etc. Two of them Northside (not bad areas) two on South side (nice areas). There are other third level colleges all over the city too.
For slightly quirky (not mass touristy) things try-
The Little Museum of Dublin
No. 14 Henrietta Street (old tenement house restored and recreated) and their tour of Northside Georgian Dublin.
Take the DART train to Dun Laoghaire a seaside town about 30 mins journey South from city. Great walk along the pier and lunch/dinner in one of the many restaurants.
DART to Malahide similar journey North, sea again, and go to Malahide Castle and grounds. Very nice place.
Walk around Merrion Square and the Iveagh Gardens.
Take the bus or DART to Sandymount, walk along the seafront, go into the village for a pub lunch. Then walk to Grand Canal Square - great for people watching and DART or walk back to town.
Get the bus to Enniskerry and go to Powerscourt Waterfall.
Avoid Temple Bar.
There are tons of other things, but I'd be here all night. Hope your visit goes well.