Well, in the new-to-me category, I have to go with Essex Green. I think The Cannibal Sea is my favorite album of the year. I'll give a nod to Camera Obscura as well and agree with the common sentiment that their album is "very good, but not great."
In the genuinely-new-first-LP-released-in-2006 category, I'm not sure at all. I've certainly liked Wolfmother, The Raconteurs, Voxtrot, KT Tunstall, Islands, Middle Distance Runner; Peter, Bjorn and John; Band of Horses, and The Black Angels. I'm just not sure any of them stand out more than the rest. I'd probably go with Wolfmother if pressed. I've probably listened to The Raconteurs more though, but I'm hesitant to call them "genuinely new."