When my husband was in law school, we looked at both the graduate housing and an off campus apartment. I understand, my situation be different from yours in that I was married at the time (assuming you're not), but we definitely preferred living off campus. We lived in a duplex that was close to campus, it almost boardered the campus property, but we were still far enough from campus. The campus itself, by its nature, seemed to lend itself to a lot of traffic.
Graduate housing posed a couple of problems where we were. First, there were a number of graduate programs at this college, business, pharmacy & law. Therefore the graduate housing was open to all three programs. A number of the business students were fresh from their undergrad and still had substantial partying to do, or so we warned by the law school admissions staff. Also, there were communal facilities, such as for laundry which is a personal issue with me. Seems like I always have bad luck scheduling laundry time with a communal facility (again a personal issue).
The duplex that we found was larger than the graduate school housing and approximately the same price. We had a 2 bedroom (one converted to a den for my husband to study), with a large kitchen and family room, private parking, and washer/dryer hookup.
Living off campus though, there are a number of things to think about. For example, depending on how close your apartment is to the campus, you may have to commute. Then you have the added fees of parking, etc. With any luck, you'd be able to find something close to school that you could still walk.
When my husband was accepted, we contacted the law school admissions office about housing. They provided us with a list of landlords/apartment communities that preferred to rent to graduate students. Their monthly rents were very competitive and the units themselves seemed to be in better condition. Most of these landlords also understood the graduate situation and the fact that most graduate students are financing their education and livelihood through student loans. Even though I was working, our landlord was very good about giving us until the student loan checks came through to pay our rent.
You may want to check with the school and see if they keep such a list. Also, check with the school and see if they have a bulletin board or space in the law school newsletter/paper where *LAW* students can post that they need a roommate, etc. for sharing a house, duplex, etc. This will provide you with a roommie on the same schedule as you who can also empathize with new challenges thrown at a first year student.