The Fitness Center at Valentin Quinta Avenida
Four Points by Sheraton Havana's fitness center is referenced by reviewers writing for major publications. Out of 3 publications that we tracked, 2 praised the fitness center, like Lonely Planet and Star Service.
Valentin Quinta Avenida 
Lonely Planet
Star Service
Lonely Planet "While there are plenty of facilities, including large rooms, gym, pool, restaurants and a business center, the lack of maintenance, patchy service and weirdly un-Cuban personality struggle to justify the price"
Star Service "There is one pool and a fitness center"
