By foot from Istanbul to Istanbul (city)
It's quite easy to walk from the cruise port to Sultanahmet in 20-30 minutes. In this district you will find the main highlights such as the bazaars, mosques and palaces. A hike gives you the chance to taste the real Turkish life.
When you leave the cruise terminal you enter an area with a big parking lot and iron gates. Once you have left that you are in Kemeralti C. or Maklisi Mebusan C., depending on where exactly you docked. There's a tram running through this streets. Follow it's track to the left. Soon you'll arrive at the Galata Bridge, where you can see the local fishermen day and night. Once you have crossed the bridge take the small pedestrian tunnel. You are now near the Egyptian Spice Bazaar. Most highlights are within walking distance from here.