hey,
I would pick georgetown over drexel - I think that g'town has a little bit of an edge - it is starting to climb again in reputation, its in a great area, there are a ton of resources in dc, and it is not all that more expensive than drexel (which is pretty damn expensive). I was not all that impressed with the facilities of g'town when i interviewed there, but it has a great match which testifies to its ability to attract its students to good residency programs. also, as the person before stated, if your gut is to go there, then you SHOULD go there- there is no better reason to attend - and better yet, if your gut says to go there, then there is no advantage to going to drexel.
I am not going to bash drexel though - i think that despite its seemingly falling reputation, it also is a good school (as is any m ed school) - people seem to really like it there, its in philly, and it has a huge technological advantage to a lot of schools - I considered going there, but when it comes down to it, you have to weigh varying factors such as debt load, location, prestige, and where you are happiest - if all point in one direction, then you have an easy decision.
I wouldn't stress about switching to g'town just b/c you settled in your mind you were going to drexel - it might be a temporary hassle finding an apt, getting readjusted, etc., but once you get there, u will be so happy.
good luck