Most of the 32 teams in the NFL carry their city name, rather than the state. The exceptions are the Tennessee Titans who play in Nashville, the New England Patriots located in Foxborough, Massachusetts, the Minnesota Vikings who play in Minneapolis, the Carolina Panthers in Charlotte, North Carolina, and the Arizona Cardinals in Phoenix.
The New York Giants and the New York Jets share Giant Stadium in the Meadowlands (New Jersey) but I believe they are both New York City-based teams. Someone can correct me if I'm wrong.
http://www.nfl.com/teams
Although the Washington Redskins are named after the city, their stadium, FedEx Field, is located in Landover, Maryland, in adjoining Prince George's County. It is the largest stadium in the league with a seating capacity of 91,000. The Redskins outgrew their former home, RFK Stadium which is located in the District, and moved in 1996. It has a football capacity of 55,672.
http://www.ballparks.com/baseball/american/rfksta.htm
Redskins Park, the team's practice and training facility is located in Ashburn, Virginia, not too far from Washington/Dulles Airport.
