This is a constantly improving sector and you should be able to find what you need in terms of sports, entertainment and relaxation either within the city or in close proximity. 
There are plenty of gyms dotted around Sofia, both small and large. Many offer group exercise classes, such as yoga, pilates, and spinning. There are also a lot of tennis courts, indoor and outdoor, though the choice of decent swimming pools and squash courts in Sofia is limited.
Big efforts have been made in the last few years to make cycling safer and more accessible with the introduction of cycle lanes in the city centre such as on bul. Rakovski and Dondukov but Bulgarian drivers are still a big risk factor. However the Parks offer a better alternative especially for families, where the biggest danger will be from dogs.
For those in search of more gentle or creative energy outlets the offer is also increasing with many activities available to non Bulgarian speakers.

Here are just some suggestions on how to spend your free time in Sofia.