The U.S. Botanic Garden is almost as old as Washington DC itself. In the Botanical Garden you can visit the Conservatory, with its fixed and seasonal botanical exhibits; the National Garden, with Mid-Atlantic region plants, and the rose and butterflies gardens; and Bartholdi Park, an outdoor garden. As most of cultural complexes in DC, entrance is free. The Garden is open from 10 AM to 5 PM everyday.
The USBG is a few minutes away from Capitol Hill on foot (you can see Capitol's dome in the background of the picture).