Oyster Club is located in Mystic, United States on 13 Water St. Oyster Club is rated 4.5 out of 5 in the category fine dining restaurant in United States. Oyster Club, located in historic Mystic, Connecticut, is a casual fine dining restaurant and raw bar specializing in the richness of the New England coast and countryside. s showcase food that travels the shortest distance from ‘farm & sea to table,’ with seasonality and location determining the day’s delicacies. Benefiting from the region’s many local farmers and fisherman, Oyster Club features bounty from the sea, pasture raised beef, local produce and artisanal cheeses, selections of which will change daily. lieve Oyster Club is an extension of your home and that all will feel welcome at our table – please join us!ations accepted for Dining Room only. Bar, Patio & Treehouse seating is first come first serve.