Driving through Mystic this afternoon, I noticed a sign on Kitchen Little saying that they are moving. A little research found out that their new home will be at the Mystic River Marina on Mason's Island, a short distance from downtown. Follow Route 1 north and turn right at the first traffic light after Sea Swirl (which is now open for the season, by the way); you'll run into the marina eventually.
Late April is the date given. I couldn't tell whether the current location is still operating during the move.