Flowing Data created several charts of sandwich chains across the 48 contiguous US states. This one makes it clear: the Subway company rules the land with a lettuce-covered fist. You can see the other charts here.
This chart removes Subway from the dataset. Arby’s is strong in the Midwest. Jimmy John’s and Panera Bread appear to be concentrated in major cities. I have not eaten at most of these delis, although I remember Jersey Mike’s as being quite good.