Sorry for replying this long after you posted, but I never get on here. I worked in the ICU at GW until September. Unfortunately, the metro does not open until 7am on weekends.
GW requires that you work about 3 weekends out of an 8 week self-schedule. Also, they require half of that schedule to be days, have nights. I couldn't handle the switching back and forth, sleep-wise, so I mostly did nights. So I never ran into a metro issue. On the rare weekend that I did work a day shift, I just drove. There is a GW parking garage that is $10 for employees.
I lived in Springfield, Va. It was 10-15 minutes from downtown DC. It was also a couple of minutes from the Franconia-Springfield metro station on Blue Line. It was a super-nice area, and I never ever had issues getting to and from work. Metro was about 25 -30 minutes, driving was 10-15.
I had wanted to live in the city, but really didn't want to have to pay $2000 for renting not-so-nice place, when I could live 15 minutes away and live in a nice place for about $1500. King Street and Braddock Road are other good options for a single female..kinda affordable and close to the metro, but also good if you bring your car.
Good Luck and congrats! Those GW ICU nurses know their stuff, it is an amazing team environment. I only left because I got married and had a baby!