I'll try to answer your question, sorry if it doesn't satisfy you. There were many kinds of entertainment in the Ottoman Empire of that era, both outdoors and indoors

Outdoors

Public carnivals and festivals accompanying celebrations or ceremonies were a popular form of urban entertainment. Such festivals contained entertainments such as staged battles, circuses, dancing, music, theaters, and firework displays. Staged battles were done to convey the superiority of Ottoman army to the public, for example the circumcision festival of 1582 recreated the capture of Kars. In the same vein, there were also equestrian shows, mock naval battles, and matrak oyuncu, a battle enactment using wooden swords. Festival circuses were also popular and is one of the main attraction of such festivals. Circuses contains acts like acrobatics, puppetry and juggling, mimicry and parody, conjuring and illusions, manipulation of fire, sword-swallowing, clowning and buffoonery, trained animals, tightrope walking, pole climbing or balancing, and feats of strength. Festival dancing were done by Mevlevi Sufis and professional urban dancers hired from the guilds, usually consisted of köçeks (effeminate boys) and çengis (women dancers). Additionally, Jewish dancers with their Spanish-influenced dances also gave a cosmopolitan color to the festival. There were also music shows to accompany the festival and dances, shadow and puppet theaters, swings, and finally, fireworks shows which highlighted night festivals. I could go on and on describing each performances in festivals (thankfully, many festivals like the circumcision festival of 1582 were very well documented) but this is just an overview and if you want to know, just ask

Another form of public entertainment/leisure is picnicking and outdoor excursions (promenading). Eating outdoors in fine weather was regarded as one of the foremost pleasures in life, and picnicking was one of the main leisure enjoyed by the Ottomans, especially women. Every town and city had its favourite public parks and beauty spots known as mesire in the nearby countryside where people went to picnic. Istanbul had 52 such places, the most renowned being the valleys of Kağıthane at the end of the Golden Horn, and Göksu, on the Asian shore of the Bosphorus. Trees for shade and a source of drinking water, whether a natural spring or a fountain constructed as a charitable endowment, were essential features of them all. At the mesire of Pınarbaşı, near Bursa, springs of water poured out of the cliffs, providing water for picnickers to drink after eating. Women were particularly keen picnickers, making up parties of friends and taking their children along. Wealthy women in Aleppo sometimes even clubbed together to rent a garden for the day, so that they would have it to themselves. When going by road, men rode on horseback while wealthy women traveled in decorated canopied wagons drawn by oxen. A cheaper form of transportation was donkeys, which women and children rode sitting astride.

Promenading, the strolling around in the gardens and open spaces both within and just outside the city, being seen and viewing others, enjoying the flowers, feasting, boating and generally relaxing in the fresh air was also a popular form of leisure/entertainment for Ottomans. Women frequented them particularly after the afternoon prayer, when the sun’s effect was less strong, or on nights with a full moon. At such times, women wandered around the gardens, or swung on the swings set up for them in suitable places, sang and enjoyed themselves. In summer, and on summer nights when there was a full moon, people sat in the little pavilions and played musical instruments and sang. Just like mesires, different areas had different reputations and offered different attractions. The pleasure garden of Yahya Efendi in Beşiktaş, for example, had many large trees, and people visited it for the beautiful birdsong of the golden orioles, blackbirds, horned owls, chaffinches, greenfinches, reedlings and nightingales. In the white cherry and chestnut season, people went to Akbaba Sultan garden, a one-day journey from Istanbul, leaving from the Beykoz jetty in thousands of carriages. Promenading and picnicking was not restricted to dry land. At night, especially when there was a full moon, the Bosphorus was filled with little boats, as people rowed out onto the waters. Sometimes special, large boats were hired for parties down the Bosphorus, accompanied by singers and musicians, and to admire the full moon. On these occasions, the Bosphorus was bathed in the sound of music coming from the boats of the many different groups. In such public spots, people such as street musicians, poets, street sellers, and fortune tellers all flocked to offer their services to the picnickers and provide entertainment. Popular entertainments such as wrestling competitions between apprentice boys, çengis and köçek dancers, folk theater and Karagöz performances, funambulist shows were also organized, and as a result gardens and promenades were never deserted.

On the Karagöz shadow-theater performances specifically, the shadow-theater is a prominent and popular theater in the Ottoman world. Members of all social classes in the Ottoman Empire watched Karagöz performed in the streets, public spots, and in front of coffeehouses. Karagöz performances tell stories ranging from traditional folktales, obscene humor, to poking fun and criticizing the state and its servants. Another kind of theater performance is Ortaoyunu, in which the crowd is seated around a circular stage on which the play by human actors is performed (though when did exactly this kind of play appeared is rather unknown, the earliest claims date back to the 15th century). The contents of the plays are similar to those of the Karagöz.