The tea gardens (çay bahçesi) scattered through Kaleiçi and along the clifftop promenade are the authentic local version of café culture. A small glass of black tea (çay) costs almost nothing; the game is to find a table with a good view and stay for as long as you like. Backgammon boards are usually available.
The best çay bahçesi in the old town are those tucked into courtyards away from the main tourist lanes. The clifftop park above the harbour has several that look out over the sea and the Taurus Mountains — find one with shade, order tea, and settle in.