A large majority of NFL fans support their local team, or the team their family traditionally supports if they have recently moved.
The instances of fans supporting a team outside their city/region is growing, however. Some teams have a larger following outside their region, but that is pretty rare.
The Dallas Cowboys were at one time the most popular team. The New England Patriots generally are disliked outside of the New England Region. The Green Bag Packers have the largest following relative to the size of their city (small by NFL standards). Other teams are 99% of their support regionally, such as the Minnesota Vikings, Atlanta Falcons, and a few others.
The Cleveland Browns have fan clubs in most major US cities, especially in the middle portion of the state. This is despite their lack of success for quite some time.
Generally speaking, the more success a team has - WITH recognizeable elite star players (Peyton Manning type) then the larger following the team receives both locally and nationwide.
I live in Indianapolis, IN and support the Colts, although I'm not a die-hard fan with multiple jerseys, go to practices or watch the draft. I didn't grow up here, which explains it I suppose. I have been to a few games, Lucas Oil Stadium is a great stadium.