University Centre is a new apartment building in Newark. It is a couple of blocks from campus and is a little less expensive than W. Market St. You must be a student of UMDNJ, Seton Hall, Rutgers Newark, or NJIT to live there (it's like a central housing thing). Web site is
www.univcentre.com. Unlike the on-campus housing, they actually DO have a gym...
Society Hill is nice, but you have to be careful in that area. If you don't have a townhouse with a garage, you are taking a risk with your car. There have been many auto break ins and such there. All of the apartments come with an alarm system and a screen door at your entrance. A lot of students do live in the complex, but it is a large complex so people are spread out. Definitely be careful and aware of your surroundings if you are thinking moving in. Also, the only way you can rent here (since they are condos/townhouses) is through the owner. Check craigslist.com or local newspapers.
That's pretty much my knowledge of the two places...