Personally for my home state, New York, I thought of the Goo Goo Dolls right away as the best band from the state ... but that also shows you where I'm from and where my loyalty lies: Buffalo. The best band according to this article in the Empire State is ... Television? Ok, I guess.
Also included in this article is Garbage for Wisconsin (from Madison ... HAD NO IDEA!), Superchunk for North Carolina, Prince for Minnesota (#shocker), and Destiny's Child for Texas.
See the rest of the list here from Thrillist for the best band out of your state!