Baltimore, MD Airport (MTN-Martin State). So much to experience, so little time. Before you jump behind the wheel of your rental car and discover the place, we'll fill you in on some key details.Once you've collected your belongings from the baggage claim area of Baltimore, MD Airport (MTN-Martin State), jump into the driver's seat of your rental car and drive into Washington. The downtown area is about 43 miles to the southwest of the airport terminal.