Palmerston Gym Directory. Click here for a comprehensive list of gyms, health clubs and fitness centres in Palmerston Northern Territory Australia. Looking for a suitable gym, health club, fitness centre, recreation centre or aquatic centre close to home or work? Click here for Australia's leading gym directory, the Good Gym Guide. If you searched for Palmerston Gyms, Palmerston Fitness Centres or Palmerston Health Clubs then click here for the Palmerston Gym Directory.