Are you referring to the place at the end of the runway at National? I think it's pretty easy to get to, just drive along the parkway heading towards town from the airport and you'll get there.
There's a lot of really good planespotting in DC b/c of the flight paths for DCA, which unfortunately is too small to take any heavy metal. But, hell, you can hang out at the waterfront in Georgetown, have cocktails at Sequoia or one of the other places, and just watch the 727s go by.
Dulles, the bigger airport, is way the hell out in Virginia, but I remember once playing golf near there and seeing several 747s overhead, albeit at pretty good altitudes. It was the time of day when a lot of international flights get in.
Hope this helps.