Georgetown is a shopper's dream come true. It is sort of like an outdoor mall, though of course it also has its own mall. There isn't a whole lot to skate in the actual town. It does have some unique terrain though. If you walk into Georgetown on M Street, past the intersection of Wisconsin Ave., and make a left down the open alley next to Dean and Deluca's, cross the bridge, and walk down the steps, there's some neat brick ramps.
The bricks that stick out, and would've messed up skating here have been conveniently broken off, so that there's a nice smooth transition. I've skated here a couple of times, and have been kicked out. I don't recommend staying for more than a half hour or so, as the people in the hotel there have been known to call the police.
There is also good skating around Georgetown University. One of the parking garages under the hospital has super smooth terrain, and it's worthwhile spending some time skating around there and exploring.