The easy route on the Asian side: a market, a high street, a seafront, a café on a pier. Kadıköy does not do big tourist sights. It does an everyday city that you'll wish you lived in by the time you leave.
Start with a ferry. The crossing from Eminönü or Karaköy is twenty minutes of seagulls and tea in plastic cups, and it's the right way to arrive. You step off at Kadıköy İskele and the city changes character — quieter, younger, more lived-in. Ten minutes south-east is the Çarşı, the market district, and its backbone is Güneşlibahçe Sokak, the fish market lane. Walk its whole length. The smells are forty different things at once and the arguments about tomato prices are part of the show.
Cut up to Altıyol to find the bull — Boğa — and then drift south along Moda Caddesi. You are looking for nothing in particular. A bookshop, a record store, the best profiterole in the country at Baylan (since 1923, don't argue). The street opens onto the sea at Moda Sahil, and the rest of the walk is obvious: follow the water until you find a bench you like. End at the old Moda pier, which is now a café. Order a tea. Earn the ferry ride back.