Woodley park is nice... if you're looking for nightlife, it's a 10-15min walk from your place to the 18th street bars (I live between the metro station and the bar/restaurant area, so I know your spot well). Just look up the interesection of 18th st NW and Adams Mill Rd on a map - that is the north tip of the strip of bars on 18th street (extends a few blocks south, along 18th).
As far as touristy things, if you want a non-generic recommendation, I thoroughly enjoyed the Newseum (history of news and journalism - basically an american history museum, but told through the eyes of the news mediums at the time). It's not a smithsonian institution though, so it's $20 to enter.
Edit: I often take family there when they visit, nothing but positive reviews.