I maintain a list of DC area rinks, with a link to an overall map, at http://mgrunes.com/dcicerinks.html
You can get to a lot of places by bus, but Wells (College Park, MD) and Kettler (Arlington, VA) are the only rinks I know of, that are open in the summer, and are near the subway.
Kettler isn't the cheapest rink, and depending on your hours it may or may not work for you, but I think it probably has the shortest Metro travel time from Galaudet.
Directions to Kettler are here: http://assets.ngin.com/attachments/document/0040/8870/KCI_Directions_4-09.pdf
Leave yourself 60 minutes more than you think it will take the first time, so you can find your way - a fair bit of walking from the metro stop. You will probably get lost if you try the "outdoor route". But it's a pretty safe area.
If you want to drive around DC, and are able to, navigating is a challenge, many roads are unmarked, parking is hard, and traffic jams in some places sometimes last 5 - 6 hours. You will need a good GPS, and a lot of patience. Also, DC makes a lot of income from giving people traffic tickets for things they shouldn't get tickets for - think of DC as a totally corrupt third world government. So Metro is a good option, if you can get to it.
P.S. I work a little at Gardens Ice House (Laurel, MD), and so should tell you to go there. But it has no metro-rail access, which I guess you want.
I regret to say that evening and weekend public sessions at all DC area rinks can be crowded. Freestyle sessions are sometimes less so, but at some rinks, including Kettler, you may sometimes have to compete for space on the ice with high level freestyle and ice dance skaters.