Interestingly, there are two states without counties-- Louisiana and Alaska. The former having parishes and the latter boroughs. They serve the same function, however, and I believe the distinction is entirely one of nomenclature. Similar to, I suppose Kentucky, Massachusetts, Pennsylvania, and Virginia being "Commonwealths" instead of states.
Anyway, geography trivia aside, what exactly are you asking, OP? The county in which a team's stadium is located, the county in which a team's offices and/or headquarters are located, the contiguous blob of counties that would constitute the area where said team is considered "local," or a county by county breakdown of who roots for which team?
Another geography tidbit. Several teams do not play in the city for which they are named--
Arizona- (formerly) While known as "Phoenix" from 1996 to 2014, the Coyotes only played in the city until 2003. Since then, they've played in the suburb of Glendale, which eventually prompted the name change.
Carolina- Technically neither a city nor a state. Like the Carolina Panthers (who play in Charlotte,) the Hurricanes were given the "Carolina" name to appeal to fans in both North Carolina and South Carolina. But "Carolina" is essentially meaningless to people in the area. The two together are colloquially "the Carolinas" and if you're in the south, people care about their distinctions. North Cackalacky and South Cackalacky don't always get along so good, as I was once told. I don't have a source on this, but I imagine billing themselves as from "Carolina" allows the Hurricanes name to make more sense. Hurricanes are frequent occurrences in both NC and SC, but Raleigh (home to the Hurricanes) is only occasionally subject to significant damage.
Ottawa- The Senators play in Kanata, not Ottawa proper.
Tampa Bay- A technicality. Tampa Bay is a body of water, and a nickname for the region akin to the San Francisco Bay Area. It usually refers to the cities of Tampa, Clearwater, and St. Petersburg. The Buccaneers and the Rays both call themselves "Tampa Bay" as well. The Lightning play in Tampa, and had originally tried to secure "Florida" when entering the name. They were denied, I believe based on the significant geographic and cultural differences between the various regions of Florida. (Same reason there are no teams simply from "California" anymore. It's just too big of an area, with too many cities that could lay claim to the name.) A few years later, the Panthers tried the same thing, but got their way on the basis that the Florida Panther is an actual animal. The Lightning were not happy about this. Ostensibly, if their claim had been denied, we'd have the Miami Panthers. (The Panthers played in Miami for their first five years of existence.) It'd be interesting to see if, in that case, if today the "Miami" Panthers tried to change their name to "Florida" as the Coyotes did (since the Panthers play in Sunrise, not Miami anymore) how that would all shake out and if the Lightning would even put up a fight anymore.