I've lived in DC proper for the past 7 years. I didn't read through all of the posts in this thread, but I wanted to stop in an offer some thoughts.
As to the poster above- rentals move extremely fast in DC. Usually nice rentals/ good deals get snatched up on the first day they are shown. This does not give an incentive to owners to put them on the market months in advance of the lease-start. I have never been able to sign on a place more than one month in advance of the lease start-date. There are exceptions to this in the large luxury-type apartment buildings.
For GULC- I would recommend Capitol Hill (Including the area near Stanton Park/Mass Ave that is very close to GULC), Eastern Market, or Logan Circle. Buses in DC are cheap, reliable, and easy once you know your routes. Good places to live (with a dog) on the Red Line would take you really far away from GULC. If you want the option of walking or biking to campus, I would focus on the nice neighborhoods near GULC rather than the nice neighborhoods on the red line. Chinatown is pretty nice, close, and on the red line, but it is not a very convenient area to live with a dog.
One note- many posters use "Capitol Hill" VERY loosely on craigslist. Be sure to verify the address is not actually closer to the Stadium or Potomac Ave metros.