It depends on what your preferences are. The majority of my North American classmates lived in the same post-graduate housing complex called Sheares Gate. They're pretty nice but they're not cheap, and you will have to live with 3 other people, usually other members of your class but you may live with upper years or Dentistry students as well. Also, they're not close to the city centre whatsoever and it's about a 40 minute walk to get there. They are pretty close to campus, and you can get to Brookfield (which is the Health Sciences building where you'll spend most of your time) in 5-10 minutes walking. Most of my classmates who lived there this year are bailing and finding houses for next year, as you're paying a lot for what you get (ie: no control over roommate selection, forced to live with 3 other people, far from town/restaurants/pubs/clubs/anything good).
Another option is Dennehy's Cross, which is also a post-graduate apartment complex. Personally, I think it's nicer than Sheares Gate, you will live with either 1 or 2 other roommates and it's about the same distance or shorter to Brookfield. Another handy thing is that it's located above a Tesco Express (Tesco is the major grocery store), so you can get a whole bunch of your groceries without going 10 feet from your apartment, and if there's anything the Tesco Express doesn't have, it's not a far walk to the big Tesco store or Cork University Hospital (where you will also be spending a significant amount of time). Cost to live at Dennehy's Cross works out to be about 500 euro a month on a 12 month lease, while Sheares is about 550 a month.
Option C is to find a house/apartment. This can get tricky since you likely won't know anyone to live with, leaving you to find a place on your own. I'm currently living on my own in the city centre, and it's definitely not cheap. A 2 bedroom apartment in the centre will run around 700-900 euro a month, excluding electricity (water is free...for now). However, it's really handy having everything around you, grocery stores are close, the market is a 5 minute walk, pubs are everywhere, you don't have to take a taxi home after a night out. The walk to campus is the only thing that's a pain, it's about 25 minutes walking fast, uphill, to Brookfield from my apartment, nearly an hour to the Cork University Hospital.
Personally if you know people coming with you, or someone who's already here, find a place in between campus and the city centre. It'll be cheaper and you'll know who you're living with. Option B is a toss-up between Dennehy's Cross and Sheares Gate. None of my North American classmates lived in Dennehy's Cross this year, just a few Irish but I will be moving there for next year, and there will be a couple more North Americans there as well. So if you want to live with people who have the same accent as you, go to Sheares Gate, if you don't have a preference, go to Dennehy's Cross.