If you have just one day to spend in Eastern Connecticut , head straight to the historic shipbuilding center of Mystic . The reconstructed 19th-century community of Mystic Seaport  is consistently rated as one of New England’s top attractions, and one of the best maritime museums anywhere. Better yet, spend several days along the southeast coastline, exploring the salty city of New London  and the historic village of Stonington .
By contrast, you won’t want to spend more than a day or two in Hartford , which has just a few sights to recommend (and closes many of its restaurants and stores on weekends). Base yourself outside the city in one of the country towns to the north or south, and dip into the urban core to see attractions such as the Mark Twain House & Museum  and the fine art collection at the Wadsworth Atheneum .
The northeastern Quiet Corner  has even fewer formal attractions, but you can easily spend a week there relaxing with long looping bike rides through dairy farms and picking your own apples at wooded country orchards. This is also one of the more historic areas of the state, with a monument to Connecticut’s state hero at the Nathan Hale Homestead  and the amazing Gothic Revival house museum at the Roseland Cottage/Bowen House . While you are in the area, blow off some steam (and lighten your wallet) at the Mohegan Sun Casino , one of two casinos on Indian reservations that have made southeastern Connecticut a gaming destination throughout the East Coast.