I was hoping I could get some suggestions on areas to live next year in DC. I am trying to live right next to the cumpus so I will have more free time. I am willing to have a roommate as I am sure that will lower the cost a little. Let me know if anybody has any suggestions.

The immediate area around the Law campus, Capitol Hill is expensive. 1500+ for your own condo, or 800+ for a room in a shared apartment.
Most students live anywhere between Georgetown (the district) and Georgetown Law (the law campus): Capitol Hill, Dupont Circle, Adams Morgan, Chinatown, Foggy Bottom, Logan Circle. If you want to stay close, take the cheapest you can find in any of these districts.

The further east/northeast inside DC, the cheaper. Used to be very dangerous areas like 10 years ago. It has improved significantly, but I still wouldn't recommend it if you're a girl, and keep your laptop in a mundane school bag rather than in a dedicated laptop case.

Anywhere on the red (subway) line is a good option too, but expect 30min+ commutes: Rockville, Bethesda in VA and Silver Spring in MD.

Students enrolled in the Foundations summer program usually find the best deals before everyone else, and they'll be looking for roommates too: try and get in touch with them (for example through lawyrs.net).