If you are planing to visit the greatest city in Turkey, do a favor to yourself and rent a car in Istanbul. A car in Istanbul save your time and you can travel more place in a day. If you can rent a car then you can do these following activities easily in Istanbul;
Rent a car in Turkish is "oto kiralama" so you can search the companies like that. Also they use araba kiralama or ara kiralama instead of rent a car.
1. Visit the Topkapi Palace;
Topkapi palace is the biggest palace in Istanbul, it is in Sultanahmet. There are 2 parts of the palace, you can visit each of them in a day. They give you a electronic guide in every main languages so you don't need a guide man.
2. Visit Ayasofya Church
Ayasofya is very near to Topkapi palace, you can visit Ayasofya when you are in Sultanahmet. Ayasofya was a great church but Fatih Sultan Mehmet turned it to mosque when he conquered Istanbul. For 50 year it has been museum and forbidden to worship. You have visited two place when you use rent a car(oto kiralama in Turkish).
3. Eat Fish in Galata Bridge
Galata bridge is very near to Sultanahmet, even you can walk 1 km to this bridge. There are lots of fish restaurant in here close to sea. So you can select you favorite fish and eat your fish with the Turkish traditional drink "Raki".
4. Make a Bosphorus Tour
When you finish your launch in Galata Bridge, you can go to Bosphorus tour from Eminonu pier. It is very cheap and amazing.