I've lived in DC for four years. If this is your first time, you, of course, want to see the monuments (Lincoln, Jefferson, Washington) along the mall. Be sure also to check out the FDR memorial along the tidal basin -- it's pretty neat with lots of waterfalls and it is often overlooked. The Smithsonian museums line the mall and they are worth checking out as well, especially Air and Space, American History, and the National Gallery (which is technically not the Smithsonian). The cafe at the Native American museum is considered to be the best, with a lot of unique offerings.
The capitol museum just opened up this year and is quite nice. Make sure to check out the Library of Congress; IMHO, it's the most beautiful building (on the inside) among all the "sites" in DC.
Ford's theatre (where Lincoln was shot) just reopened with a new museum and it's very good, as is the Newseum, which has some interesting (and moving) memorabilia, such as the radio tower from the World Trade Center and a huge portion of the Berlin Wall.
The White House is nice to look at, but they don't give tours anymore (unless you write to your congressman).
The best part about DC is that most museums and sites have free admission.
Off the beaten path, Eastern Market on Capitol Hill is very nice to walk through on weekends, with lots of vendors, crafts, food, art, jewelry, etc.
If you like churches, be sure to see the National Shrine Basilica on the campus of Catholic University (largest church in North America), St. Matthew's Cathedral, and the National Cathedral.
As far as hotels go, it is a little difficult to find cheap places downtown. The Marriott Courtyard Convention Center is pretty centrally located. If you don't stay downtown, get a hotel along the metro line, which is super convenient, safe, and clean. Staying in Rosslyn (Key Bridge Marriott or Courtyard) or Clarendon can be cheaper sometimes.
Important restaurants you should check out: Old Ebbit Grill (next to the White House), the Monocle (where many members of Congress eat lunch and dinner), and Ben's Chili Bowl (important location with respect to the race riots of the late 60's -- every travel show goes there for the "half-smoke" sausage).
Oh, and if you want to get out of DC for a little bit, be sure to see Mt. Vernon (George Washington's house), Old Town Alexandria, and Great Falls Park, all about 15-30 minutes away.
Hope this helps. If you have any questions, feel free to ask. Have a good trip!