How about if it's sitting up looking at the starry sky with binoculars...?
Actually, the first things that come to my mind which relate to SETI would be 1) something that looks like a non-human (ok, cheetahs sort of qualify), or 2) a radio telescope dish. Either way, nothing really springs to my mind in the way of a mascot, exactly. For a logo, one of the mad l33t Photoshop geniuses like
Beefcake could probably blend together some images and make a truly excellent logo. Did you all see
narzy's logo that he cooked up just recently?