Agreed. I'd recommend visiting Mystic, Stonington or Essex, CT and stay in a historic inn or B&B instead of a with a hotel chain.

Fairfield County, e.g. Stamford and Norwalk where there are SPG hotels, is basically a bedroom county for NYC/Stamford commuters with several exceptions, and I wouldn't recommend staying there for leisure since there isn't much to do. Eastern CT has more leisure options (quaint towns or Mystic Seaport and Foxwoods/Mohegan Sun gambling if you're into that). You could also take a ferry from New London to Block Island for a day or two.