If you get somewhere provided by your school, I would recommend you take it. It may not be a palace but it will give you a base to get set up, make friends and explore Dublin at your own pace rather than hunting all over a strange city for a house. Next year(s) you can share a house with your new mates. Living on your own is expensive.
If you do not get somewhere to live provided by your school, try this site
www.daft.ie
and click the College tab in the Lettings section.
I would advise against living more than a 3 mile radius from your school unless you are on a rail/tram line as traffic in Dublin is pretty bad.
If you are in RCSI, the Luas tram green line stops outside your door so somewhere on that route is good. Lots of new apartments in Dundrum near the new shopping center.
http://www.luas.ie/green-line.php
Trinity is well served by bus routes and the DART rail stops at the back door.
http://www.iarnrodeireann.ie/dart/home/
http://www.dublinbus.ie/home/
UCD will probably give you campus accommodation but if not, it is well served by buses and there are lots of residential areas around it to rent in.
The southside is generally a better place to live. Some areas are quite expensive (Ballsbridge, Donnybrook, Ranelagh) but you can find cheaper suburbs near those areas. I would avoid the north inner city.