Purchase a ticket and join the crowds at a game at XL Center. If there's nothing happening while you're in town, you might like to check if they offer a tour of the grounds.
Pay the entrance fee for XL Center and explore at your own pace. You'll find this sporting facility in the riverside district of Downtown Hartford. After you've had your fill there, this area has tons more to offer — Mark Twain House, Bushnell Park and Xfinity Theatre are also worth dropping by.