it's really hard to find a place from a distance. i took a couple days to visit DC. went to 6 different visiting appointments for apartments and ended up loving the last one i visited and doing the application that day.
in response to all those people starting at georgetown in the fall. the glover park area is nice and affordable, especially if you have a roommate. depending on where you are in this neighborhood it takes 15-25 minutes walk to get to the english building on campus. it's residential and very safe, so it might not feel "cityish" enough for some though it's right by wisconsin ave, which has restaurants, bars, cvs, whole foods, safeway, etc... also i can be in dupont via bus in 20 minutes either to go out or to take the metro somewhere else.
several people in the program over the past couple years, have lived in "bernstein management park crest apartments," they are really spacious, pet friendly, utilities included.
obviously craigslist is a great place to look, but a lot of corporately managed apartments (like the one i live in) don't list there. furthermore--you have to balance cost vs comfort. so yes, i'm a bit farther from school than a basement studio actually in georgetown would be, but i also don't mind the walk and prefer having space to spread out.
pm if you have any specific questions and i'll try to answer as best i know. good luck!