Not a drop-in gym for a short trip — the site names three ways to join (month-to-month, prepaid year, year contract) and no day pass. Worth a call if you're renting nearby for the season, not for a weekend.
gym · Bridgehampton
Gotham Gym
The Hamptons outpost of the West Village boxing-and-training brand (also in Miami Beach) — cardio equipment, free weights, squat and bench racks, 45-minute boxing/conditioning group classes and private 1:1 sessions with in-ring trainers. Membership is month-to-month, prepaid annual, or a year contract; exact prices aren't published.