Depending on what you're into, where you're staying, and what your budget is, here's a nice list of stuff to do in DC. I've lived here for 3 years now and STILL not hit everything, so just take your time and enjoy. Some of this will also depend on weather. I put the neighborhoods next to restaurants/bars so it makes it easier to find
Sightseeing
-Washington Monument, WW2 memorial, Tidal Basin (Jefferson, FDR + MLK memorials), Lincoln, Korean War memorial, Vietnam Wall. Lincoln at night is one of my favorite places in the city
-National Cathedral
-Iwo Jima and Arlington National Cemetery in Arlington
-Go up the Washington Monument if tickets are available
-Natural History Museum, American History but only for the flag. Most of the AH museum is under reno right now and thus rather disappointing. Air and Space is meh, the good stuff is out at the Udvar Hazy Center in Chantilly, VA
-Holocaust Museum
-Newseum. You have to pay for this, but it's well worth it and will take you a solid 3-4 hours to get through. The 9/11 portion will make you cry.
-National Portrait Gallery in Penn Quarter. Houses the only complete collection of presidential portraits outside of the White House and has a killer atrium.
-Mount Vernon if you have a rental car and the weather is nice
-Gravelly Point (just off of the GW Parkway) if you have a rental car and the weather is nice
-Old Town Alexandria
-Eastern Market
Food/Bars
-Zaytinya (Penn Quarter) for Mediterranean tapas and the best pita bread you'll ever have
-POV at the W Hotel (White House) AT NIGHT for expensive cocktails but the best view in the city
-Off the Record at the Hays Adams (more expensive cocktails)
-Ethiopian: Ethiopic. Mexican: District Taco (13th & F) or Oyamel (Penn Quarter). Spanish: Jaleo (Chinatown). Indian: Rasika (Penn Quarter). Thai: Little Serow (Dupont) or Doi Moi (Logan Circle). Southern food: Vidalia (Dupont). Steaks: Rays the Steaks (Arlington, VA). Burgers: Shake Shack (Chinatown, Dupont), Rays Hellburger (Arlington, VA). Pizza: Pizza Paradiso (several locations). Retro food: Ted's Bulletin (epic homemade poptarts, Capitol Hill). American food: Clyde's (Georgetown), Old Ebbitt Grill (White House), The Hamilton (White House). BBQ: Hill Country (Penn Quarter).
-If you like beer, you must hit Churchkey (Logan Circle). If you like bourbon/whiskey, you must hit Jack Rose (Adams Morgan sort of).
-Other good bars: 1905 (U Street), The Brixton (U Street), The Gibson (U Street), Marvin (U Street), H Street Country Club (has a small DC-themed mini golf course upstairs, H Street), The Big Hunt (dive bar, Dupont), Meridian Pint (Columbia Heights), Hawk and Dove (Capitol Hill), Millie and Al's (dive bar, Adams Morgan)...the list goes on and on.
Avoid at all costs: Ben's Chili Bowl pre-3 AM, standing on the left side of the metro escalators, DC taxicabs.
Walk left, stand right, and welcome to DC