Metro has ALL your needs covered, bro.
Take the Metro from the Reagan DC airport.
$6.50 for an all day pass.
http://www.wmata.com/
to get here:
http://213.138.148.37/doc/en/contact/driving.html
Get on the
Yellow Line at Reagan DC airport and go to
Metro Center and get on the
Red Line. Take the
Red Line to
Shady Grove and get off at the
Zoo / Adams Morgan. Is a longish walk, but saves you money.
Use this map if you get confused:
Map of Metro