IAD is a poor airport for public transportation options. Given your situation of having lots of stuff and several people, I'd say taxi is the definite option. Rental car is another option, though navigating the streets in downtown DC is not the easiest thing to do for a visitor, especially when jet lagged and/or if during rush hours. It is easy to drop off a rental car in downtown. For example, Aviis has 3 locations in central D.C., but note that these locations have much more restricted hours than airport locations and that purchasing gas in downtown DC isn't so easy (there are only a few places).
As for things to do in DC, there are other existing threads on that topic. You might want to check out the NASA website as NASA headquarters is very close to the National Air and Space Museum. They may have a gift shop, information center, etc. Also, Goddard Space Flight Center is in the D.C. area and note that there are two branches of the National Air and Space Museum and that one branch is located at Dulles Airport itself.