THIS CLUB HAS IT ALL! Eastern Athletic Club. Eastern Athletic Club is the premier fitness and health club in Carteret County. 18,000 square feet and approval for another 12,000 square feet for expansion. Competition indoor heated pool, tanning facilities, massage therapy, rehabilitation services, steam room, hot tub, cardio equipment, strength training equipment, free weights, aerobics, nursery, FM cinema TV's, locker rooms, lounge and snack/juice bar.