I haven't been to DC since 1997 and H has never been so while in NY I jumped at the chance for another trip.
We took the train from NYC and in about 3.5 hours we were in Washington DC. The day we arrived was wet and miserable, the day we left was cold but clear. But that worked perfectly, a day for the Smithsonian's (indoors) and a day for the monuments (outdoors).
W Washington DC, small rooms (tiny) but in a great location, within walking distance to everything
Cafe du Parc, the place where Kevin Rudd resigned as foreign minister
Old Ebbitt Grill, a popular place for oysters and a steak
You have to pick your museums, so with half a day spare (the main ones were open til 7:30 pm the week we were there) we visited Air and Space Museum and the Natural History Museum
Visit the National Tree depending on the time of year
Walk the monuments, leave 2 hours to walk the full circuit (but missing Arlington). Two of our favourites was the Korean War Veterans Memorial and the Lincoln Memorial
DC is a fabulous city and you could stay a week and not run out of things to do or see.