Try an off campus apartment, because often they are cheaper, and as a graduate student, you probably don't want to live with a bunch of undergrads.

I know kids who are currently in grad school because they graduated a semester early and are still living in their undergraduate housing. They stayed because they didn't want to miss out on the last bit of undergraduate life, even though they've moved on in school. This is where all of their friends are.

I personally will be living off campus during grad school. It's very likely that where you go to school, off campus housing will be cheaper and more distraction free. Don't underestimate the increased difficulty of grad classes. They really are considerably more intense, I'm enrolled in one now as an under grad. Plus you don't want to be that creepy kid who graduated last year but still goes to all the undergrad parties...

If you're looking for ways to convince your parents, you could argue that access to the library and working in groups would be much easier from on campus housing. As well as the amenities that are available such as the gym, food services, parking, safety etc. I would go with trying to convince them that it's either better economically or will improve your grades.

As a graduate student, I do not live on campus. However, I am married with a child...would be a little difficult, don't ya think?

It really comes down to personal preference. But, I think the closer you are to the campus buildings, like the Library (where us Graduate students spend a massive amount of time) and the Dining Hall, the easier life will be for you. A lot of universities offer floors or even whole dormitories dedicated to Graduate students. If the school you are looking at offers that, its a great opportunity to immerse yourself in a community of fellow students who are in the same situation(s) as you.

It may be cheaper to live off of campus, but I think for convenience sake, living on campus is a wiser choice.