You basically have three airport choices. Reagan (National, DCA), Dulles (IAD), and Baltimore-Washington International (BWI).
Reagan is closest and most convenient to the hotel.
BWI is further away, but is a Southwest hub and tends to have the cheapest prices. We love Southwest because they don't charge for luggage, and because changing or cancelling flights is free. As Donna says, getting from BWI to the Hyatt is pretty easy and cheap; there is a commuter train from the airport to Union Station which is a few blocks from the hotel. The train is about $7.
Dulles also tends to have relatively cheap flights (SW goes there, too). It is a pain to get downtown from there. As Josephine describes, it is inexpensive but time consuming, especially if you have luggage. A couple of transfers are involved. Another choice is
the Supershuttle. It will take you in a van, door-to-door from the airport to the hotel. Price should be about $29 one way. If you are travelling with others, it is an especially good choice since additional passengers are about $10.
So, Steven,... a lot comes down to the actual cost savings to fly into a more distant airport...and your stomach for hauling your luggage around.
