Istanbul is a big and interesting city and in terms of entertainment it is very rich. I will list a few of those places where you can have fun and relax, excluding excursion programs, as you requested:
Aqua Marine and Aqua Delfin water parks, Istanbul Dolphinarium, Baromoglu Zoo, Mycik Ice Museum, Istanbul Aquarium, Juraysik Land Entertainment Park.
You can also entertain yourself with the famous fishing on the Galata Bridge, walks along Nevizade and Istiklal streets, where you can see a lot of interesting things and make bargains.
And in the evening, be sure to visit a variety of narghile cafes and nightclubs, of which I can advise “Babilon”, “Goedet” and “Reyina”. By the way, there is also an interesting frequent phenomenon in Istanbul – jazz cafes and jazz clubs, visiting them will impress you! Jazz is very pleasant, but in some kind of its own, Istanbul style, or something.
And then, I’ll tell you, be sure to visit the Istanbul baths – a hammam, an unforgettable experience, a real buzz for body and soul, I advise Galatasaray and Chaaloola.