For a fun underground speakeasy, we highly recommend stopping by The Alex at the Graham hotel in Georgetown, DC. Tell the bouncer at the door or the concierge that you're there for The Alex and they'll give you a passcode to enter the hidden speakeasy.
Going to a Nationals baseball game is a MUST when visiting DC! From June 10 to June 19, the Nationals will be playing at home in DC, so try and stop by for a game if you have a chance. From June 10 - June 12, they're playing the Milwaukee Brewers. From June 13 - June 15, they'll be playing the Atlanta Braves. From June 16- June 19, they'll be playing the Philadelphia Phillies! Obviously I'd recommend not going to the game on June 18th :)
Unlike in New York and other cities, the museums in D.C. are usually free! They're also captivating for people of all ages. All of the Smithsonian museums are worth stopping by, but some of our favorites are 1) Museum of Natural History, 2) Hirshhorn Art Museum and Sculpture Garden, 3) National Zoo, Smithsonian Gardens, and 4) the National Air and Space Museum Udvar-Hazy Center (in Chantilly, VA!)