Olde Mistick Village & Mystic Aquarium make a classic family day across the Connecticut line. The village is an open-air, colonial-style shopping destination with more than 40 independent shops and eateries, a duck pond and free parking. Right next door, Mystic Aquarium is home to beluga whales, sea lions and penguins, and it’s mostly indoors, which makes it a perfect rainy-day plan.