Mandarin would be the closest to the Holocaust Museum. Great hotel, but the 'neighborhood' leaves a lot to be desired - not bad, just not much happening in SW (I work nearby). Once you got your fill of the Mall-based attractions (for which the hotel has a good location), you'd likely find yourself driving or taking a cab - especially for anything at night/weekend after hours.

Monaco is in a good location - a lot going on around there these days, closest to the Spy Museum, and a quick Metro ride up to the zoo. Not too far from the Mall museums, too.

Some off-the-beaten path ideas that might appeal to a 13-year-old: "The Awakening" statue at the tip of Hains Point, as well as a stop off at Gravelly Point, just north of National Airport off the GW Parkway - best place to watch planes landing right overhead. The National Museum of Health and Medicine at Walter Reed is supposed to be good - if you're not too squeemish - but haven't gotten there myself, so only going on second-hand recs. If you seem to have booked too much time, you can always explore the environs - stuff like hiking the Billy Goat Trail at Great Falls, day-tripping to Harpers Ferry or Gettysburg, or trekking up to Annapolis to take in the Naval Academy and pound some crabs.