Because of the relatively short distance between New York City and Washington DC, air travel is rarely the best option for travel between the two cities. In cases where it is, many airlines offer routes between NYC's three airports (LaGuardia, JFK, and Newerk), and DC's three airports (Ronald Reagan Washington National Airport, Dulles International Airport, and Baltimore Washington Thurgood Marshal International Airport). Since air travel involves getting to the airport early, dealing with security and baggage, and traveling to and from each airport, the gains in travel time are minimal for the (typically) higher cost of travel.
Our air section has more information on traveling from each of DC's area airports to the city itself. Travel from BWI (often about an hour) further negates the benefits of air travel. However if time is a priority, the trip between the closest airports to your final destination can make the trip between cities only a couple hours.