i just graduated from the elliott school's undergraduate program and i took quite a number of its graduate level classes to fulfill my requirements. although the school has amazing and well respected professors, it's academic quality can sometimes be questionable. most importantly, the professors and staff are extremely supportive and willing to help their students find internships/jobs and write letters of recommendation.
as an undergrad, i was annoyed that the classes were late at night and that it met once a week for among 2 1/2 hours to 3 hours but it makes sense from a graduate perspective. the graduate classes are set up in a manner that allows the students to work during the daytime and study in the evenings.
furthermore, the location of gw is prime - it is located so close to the state department, csis, brookings institute, pearsons institute, human rights watch, etc. during my college years, i had a number of internships at a couple of think-tanks and i noticed that gw probably has the largest reach and connections within these institutions. for instance, many of the research fellows and program members at the wilson center and csis were alumni or professors at gw.
overall, i highly recommend going to gw but this is also coming a recent graduate who may have a biased opinion of her alma mater. i wish you luck with whichever choice you make and congratulations.