I don't deny that there is a huge variety of American accent, it's just that I was under the impression that most American accents were more monotonous than British accents, although I was listening to an Englishman yestereday, and he sounded also very monotonous so I guess the reverse is true as well. In fact, it wasn't even a valid point to begin with.
But yes, the variety is huge, and the more I listen to American speech, the better I am able to recognise where someone is from. For example, I can recognise a New York accent if I hear someone speak like Woody Allen or George Costanza (the character from Seinfeld), although I'm not sure if that's a typical New York accent or not because I've heard different people from New York who sound completely different.
I can also spot the Boston accent, which has a very typical -art sound, in words such as smart, party. I don't know when I was first exposed to this accent, but a couple of years I ago I saw a movie called The Town, in which the actors speak with a Boston accent.
Barb_D mentioned Fargo. I saw this movie a long time ago and I don't remember the accents very vividly, but since then, I have learnt that Minesotans have a very characteristic "o".
I have only scratched the surface, but these are examples of movies Huda-M and Over the Top can see to really hear how one American accent is different from the other.