This post is based on--heck, totally stolen from--the 36 Hour series produced by the New York Times. If they send a cease and desist order, well, I’d have to agree that I pretty much copied the idea and would have to comply. Although, technically, this is called the 37 and One Half Hour Series. Click here for Day One.Day Two
Morning: Up early, yea? Skip the petit déjeuner offered at the hotel. Head to U Street (Green Line on the Metro) and get a hearty breakfast at Ben's Chili Bowl or Mocha Hut (1213 an 1301 U St NW). There is some shopping and sightseeing here, with the highlight being the African American Civil War Memorial (Vermont and U St NW) This memorial's name pretty much says it all. It's a nice departure from the heroic style single subject memorials of downtown. Other attractions are on U Street NW between 16th and 10th Streets and on 14th Street near U St.
If you are a museums person realize that you can't see them all. Go with your gut and visit those you think you'll be enriched by and enjoy. And even then, chose an exhibit or two and just see those. I have to recommend my favorite two art museums, the National Gallery of Art and National Portrait Gallery. The Portrait Gallery (8th and F Sts NW) is part American history museum, too. The permanent exhibit, America's Presidents, features timeless portraits of every commander in chief (besides Obama, he hasn't gotten an official portrait yet). The National Gallery (4th and Constitution NW) offers classic and modern art from around the world and never ceases to showcase the best of its vast collections. Spilt time between both of these distinctly different, but equally enjoyable museums. Lunch at either: National Gallery's quaint throw back cafeteria with neat views, or the covered courtyard at the National Portrait Gallery.
Afternoon: No visit to DC is complete without a visit to the peoples house, the United States Capitol Building. Secure a tour of the building in the Capitol Visitor's Center. Consider skipping the exhibits in the center itself and get the earliest tour possible. It's one of two ways to get into the Capitol Building. The other is to get gallery passes from one of your Congressional representatives. You get to watch what passes for debate these days up close and personal. Score passes in advance if you can and do this instead of the fixed building tour. Time is always an issue, but if you've got it, make a proper visit to a Senator or House Representative. We don't have either as residents of a federal District; and regardless, I think if you're in DC , try to connect with your elected leaders and lobby for a cause of yours. At least sign the guest book.Again with the time, you'll be running out of it at this point. Squeeze in a quick photo-opish visit to the Supreme Court or the Jefferson Building of the Library of Congress. They are a block apart from each other (1st and East Capitol Sts) and are impressive architecturally and symbolically, although you can't photo the inside of the SC chamber.
Get some rest at the hotel and get ready for a night on the town.
Every guide to DC urges visitors to wade out of their comfort zone and visit one of the in-town neighborhoods. Something off the beaten path. Adams Morgan's bars, Dupont's people watching., or Georgetown's cobblestone. I think all those are doable and I do think that out-of-towners visit those place and find them interesting. But if you want something different, they Atlas District on H Street NE between 12th and 14th Streets. Take a cab from the Gallery Place Metro, Union Station Metro, or where ever you are and be prepared to take a cab back to where ever you are sleeping. Have a number of a company you can call in advance of needing a ride home. Palace of Wonders offers shows that can't be found anywhere else this side of New York City. Eat out at Sticky Rice, Jimmy Valentine's (1103 Bladensburg Rd. NE) or Granville Moore's (1238 H Street NE). Then party party party the night away there or Rock & Roll Hotel, Red and the Black or H Street Martini Lounge (1353, 1212, and 1236 H St NE respectively). Bars close at 2 on weekdays, 3 on the weekends. Not saying out have to stay out that late... just make sure you have that cabbie's number handy. 
