The monuments are a no brainer, if you're into planes and such there is a shuttle from the Smithsonian to the air and space museum out near Dulles as well.
I live in the area and have basically my entire life. There is lots to do and all depends what you consider a fun time and time constraints.
Staying in DC is murder on price but staying in Arlington or Alexandria would be cheaper and metro stops are close so transportation isn't a huge deal, and honestly that is better than driving in the city.