One of my favorite covers is a cover of Jar of Hearts sung by Sam Tsui. He is just amazing. I love his voice haha. You should check out the band Mumford and Sons. They don't vary a lot in sound on all their songs, but I really like their sound. A lot. Haha.
If I actually think about it, a lot of my FAVORITEFAVORITE bands aren't even American, or they have strong ties towards other cultures. Like The Script and Mumford and Sons are both Irish, one of the members of 3oh!3(i forget which one :?) has dual french-american citizenship.
Then from there, my favorite US bands tend to come from California. Green Day, Rancid, The Offspring, Smile Empty Soul, Fang, Metallica and a bunch of other bands like that. Haha. I really like all the Punk/Rock that came out of Berkley.
I also like a lot of the Indie Rock/Alternative Rock that is coming from LA these days, and not that generic crap that you hear on the radio.