North of Downtown is Dupont Circle, the trendy and gay district of Washington DC. You can reach the area with the metro (Dupont Circle stop, Red Line). To move around, you can follow a walking tour. Go to the tourist office and ask for a brochure of Dupont Circle. In Dupont Circle you can see some nice apartment buildings, and the Embassy Row.
A good place to start the walking tour is at 18th Street and Massachusetts Avenue, east of Dupont Cirlce Square, where the National Trust for Historic Preservation is. This house was originally built in 1915 as the McCormick apartment building.