You won't have a problem spending a week at the Smithsonian! Guess the big 3 are the Natural History Museum(lots of gemstones, etc.), Air & Space Museum(lots of original aircraft hanging from the ceiling), and American History Museum with old cars, inventions, etc. Be ready to do LOTS OF WALKING in the mall area. You can see the White House from the lawn of the Washington Monument. For some reason I don't have much desire to tour the White House these days. Besides the museums, other nearby attractions are the Library of Congress(beautiful ceiling and ar****ecture just on the other side of the Capitol building), Capitol Building(where all the bad laws are passed), multiple memorials and monuments(Lincoln, Washington, Jefferson, etc.) which stay open after hours and can be seen in the evening, Vietnam memorial, etc. There's also the Federal Reserve building where the currency is printed and the FBI building both of which offer tours, as well as the National Archives building which houses the Declaration of Independence, etc. Not much parking in this area....much better to park at an outlying subway station and use the nice subway system to get you everywhere. Outside this area across the Potomac(yup, the subway goes under the river too!) is the Arlington Cemetery with Robert E. Lee's home up on the hill. Can't miss the changing of the guard ceremony which happens every hour or so. Pentagon and Iwo Jima memorial also in this area. Further out of town there is George Washington's Mount Vernon estate and home.
As for New York, don't miss the Statue of Liberty, Empire State Building, Times Square(watch for any odd-looking packages or vehicles sitting around
), twin towers were nice
, Wall Street, etc. If at all possible, drive up to Buffalo area(easily done in a day) to see Niagara Falls. Food doesn't stick out in my mind since we didn't spend enough to eat at the fancy restaurants. Now the lobster and scallops in Maine.......wow!