The graduate and undergraduate phases of higher education have enormous differences between them. The most important distinction is also the most obvious: graduate school is more academically strenuous than obtaining your undergraduate degree. With this comes a whole mess of other considerations that will affect your choice of living conditions.
Getting Your Schoolwork Done
Your graduate studies are likely to be more difficult, time-consuming, and possibly stressful than your undergraduate studies. Your considerations of where to live should include finding a place where you can get some work done. On the other hand, if you don't mind spending a lot of your time at the library to work in peace and quiet, maybe you can trade that aspect off for something more important to you (like lower rent). As long as you plan ahead, you should be okay.
Being a Busy Person
Graduate classes are generally at night. This is because a lot of people who go to grad school work full-time. This may be the case for you, and you ought to consider that when choosing a place to live. First of all, you need to be able to sleep if you are working full-time and going to school. You'll also want a place that is easily accessible between school and work.
Graduate Housing
Your undergraduate years were probably full of self-discovery, shifting social perspectives, and at least some recklessness. Not that any of that really goes away, but you are likely to be a little more "settled" by the time your graduate years start. For this reason, and those listed above, it is unlikely that a regular dorm will best fit your needs. Although, something like being an RA could give you, essentially, free rent and a place to yourself.
Some schools have housing specifically for graduate students. It might be more apartment-style living or houses on campus that the school owns. This could be a more affordable option that has the added benefit of being close to where your classes will be held. The culture there is likely to be more studious and understanding of the particular needs of a grad student, and you might even get to find some study buddies.
Going to graduate school can be stressful enough as it is. Try and find a place to live that eases this stress, rather than adds to it. That way, you can live your life and get some sleep.
