I live in DC and can say that I've taken friends (who haven't ridden in city traffic before) out riding with me with no problems.
Early on the weekends, the traffic downtown is light so you shouldn't have any issues, depending on where you're going. The area around the zoo can be a bit hilly going north, but going south towards downtown and the Mall will be a breeze. cc_rider is right that riding on the Mall at night is great - from there it's only a couple minutes biking to the White House.
There are lots of bike trails in/around DC if you'd like to do some off-street riding. Google Maps will help you out now that they have bicycling directions. You can also take the (crowded) Mt. Vernon Trail to Gravelly Park to watch the airplanes take off right overhead.
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