You might want to go to Dumbarton Oaks on the northside of Georgetown.
Extensive gardens and beautiful grounds.

http://www.doaks.org/

The Rose Garden (National Garden) next to the United States Botanical
Gardens is not planted yet, but it is still well worth the trip there. Right
on the National Mall next to the Capitol Building. VERY neat building with
tons of plants - Bartholdi Park is right across Constitution Avenue from the
"Big Greenhouse" - Lots of plants and quite a few rose bushes. I live 2
blocks from there, must see if you are traveling here.
http://www.usbg.gov/