I've lived in the DC area for 32 years, so I qualify as a local.
I think the Lincoln and Jefferson Memorials are best experienced at night. You'll be safe, as the monuments are open until midnight, and quite a few tourists are at both sites until closing.
Another thought about visiting Washington--if you have a connection to a US address, contact the senators from that state and the congressman who represents that zip code (you can go on the
www.house.gov website to find out who), call 202-224-3121 (the main Capitol switchboard) and ask for that congressman's office, and see if the staff there can't set you up with VIP tours of the Capitol Building and the White House (they call them VIP tours, but anybody can get on them). I think the White House tours have resumed after the hiatus after 9-11. Both places are incredible and ought to be seen. You also ought to try to get a tour of the Supreme Court building, as it is beautiful inside (the Supreme Court is opposite the east front of the Capitol). Just south of the Supreme Court is the main building of the Library of Congress--the main reading room in there is worth a visit too.
The great thing about DC is that all the major public attractions arrayed around the Mall have free admission. This includes all the Smithsonian museums, and the main hall of the National Archives, where the Declaration of Independence and the Constitution are stored and can be viewed through glass.
As far as eating, tourists ought to see the "Old Ebbitt Grill", on 15th Street between F and G, across the street from the Treasury Building, the Dubliner, at North Capitol Street and Massachusetts Avenue, NW, and Kelly's Irish Times, which is just west of the Dubliner. The latter two places are terrific Irish-style restaurant/pubs.
Enjoy.