The İDO and Şehir Hatları ferries between the European shore (Eminönü, Karaköy) and Kadıköy on the Asian side run throughout the day and into the evening, carrying commuters, tourists, and fish sandwich vendors. The journey takes about 20 minutes across the Bosphorus and is worth doing even if you have no particular plan for the Asian side.
Take a seat on the upper deck for the best view — the minarets of the old city receding behind you as the Asian shore comes into focus. The tea vendor on board sells çay in the traditional small glass; the combination of salt air, tea, and the spectacle of one of the world's great waterways is very hard to improve upon.