Fairfield County Hunt Club | 51 followers on LinkedIn. Private year-round country club with dining, social and sports activities for the entire family. | Welcome to the Fairfield County Hunt Club, a private year-round country club with dining, social and sports activities for the entire family. The facility is located in Westport, CT on 40 acres of scenic property that includes a newly renovated clubhouse, stables, indoor riding arena, tennis courts, paddle tennis courts and swimming pool.