Mohammed, there are various activities you can do in Baku. People here are very friendly and usually we prefer spending our time around friends and relatives. So, most common "activity" you would find here is people having walk or sitting in cafes/pubs/tea houses. Men spending time playing games while drinking tea, chatting, smoking hookah and etc.
However this is not even near to the list of activities you can have in Azerbaijan. Some of them which I personally do quite often.
- Go for a walk (boulevard, parks and etc)
- Nature is definitely worth seeing outside Baku. Like Gabala, Guba, Gusar, Sheki, Zagatala, Lenkeran and etc are good places to visit. There are various tours for quite reasonable price.
- Visit interesting places around Baku (mud volcanoes, burning mountain, Gobustan, Oily Rocks are unique in the world and you would not find them often.)
- Skiing in winter. New skiing resort is ready in Gusar for cheaper prices with European quality.
- Cycling in or outside city.
- Join some activity clubs (travel, cycling, car enthusiasts and etc). They usually organize some group activities.
- Gaming and fitness clubs such as "Olimpik star", "Baki Eylence Merkezi" and etc where you can play billiards, pool, ping-pong, bowling and etc.
- Go to swimming in pools in winter and sea on summer.
- Ride karts with friends.
- Dance in night clubs. There are increasing number of world famous DJ's visiting Baku like Armin van Buuren, David Guetta, ATB...
- There are usually quite interesting events/concerts - Jazz club is good for jazz lovers, some instrumental and dance shows (Erisioni, Fire of Anatolia, Keiko Matsui and etc have regular shows in Baku)
- Listen to mugham in Mugham center or elsewhere.
These are just what I came up with while writing this post. I am sure you can find dozens of other activities for your interests.