The best and most memorable dining experiences I've had in Connecticut has been the omakase at Otaru sushi in New Haven. The quality of the meal and service is a bargain when compared to similar offerings in New York City, where the chef and owner worked before starting his own place here. I've eaten at Union League, Millwrights, Tavern in State, and many of the other places listed in the comments. Otaru bests them all, in my opinion.