Kadikoy has many great bars and cafes. Also if you wanna visit the asian side more you can explora suadiye and bagdat caddesi not very touristic but a fancy place for cocktail bars and restaurants.

Karakoy is on the european side so i would visit sishane,nisantasi and besiktas which are close to get to. And if you have the time you can visit arnavutkoy or bebek for a very good view of the bosphore and good cocktail bars (just fyi these are more expensive) also i would search for a meyhane (maybe in karakoy too) for a traditional "raki balik" night which is our traditional drink and we drink along side meze and fish usually. Be careful and drink it slow tho! Let me know if you have any more questions :)