--gyms are everywhere. Check some of the popular hotels. I know that ISR plaza (located behind Mcdo. fountain square)has one and it is quite cheaper than the rest, Landmark Hotel (lots of expats), Hyatt gym is also full of expats and locals. Go to Otto pub, meet loads of Turkish guys who might know a good place for you.
--swimming pool- most of the big hotels here normally open their swimming pools in the summer. Excelsior hotel, Hyatt, Ramada hotel, ISR/ Radisson plaza, not sure with Hilton (I haven't been there.lol) If you fancy a place that is quiet, go to Aqua park in Novkhani.
In " Green Spa&Fitness " Center Discounted Prices!
Limited Swimming Pool( 3 times in a Week Usage of Swimming pools, Jaccuzi, Sauna&Steam Room)1 month-100AZN!
Limited Gym(3 times in a Week Usage of Gym) 1 month-100AZN!!!
Contacts: 0772777482; 0772777481; green_spa_fitness@mail.ru
Articles to help you in your expat project in Baku