I recently visited Istanbul as well. Too my surprise, I ate the best burger I had in my lifetime. It was a smash burger joint in Emirgan district. Forgot the name. but remember finding it on google maps. Give it a try if you are passing by.
A good burger place in Turkey? Best in your life? Please do try to remember the name. I'm gonna be honest with you, I don't think there's a burger place that's that good but i'd love to be wrong about it.
I had to google it but found it for you. It was this place: https://goo.gl/maps/cEEk21F9nP5rMvAG8