The Historic Areas of Istanbul were added the UNESCO World Heritage list in 1985. The designation includes sites such as the Hagia Sophia, Topkapi Palace, Galata Bridge and Suleymaniye Mosque and is divided into four zones: the Archaeological Park at the tip of the Bosphorus Peninsula, the Suleymaniye Quarter, the Zeyrek Quarter and the zone of the ramparts. While all four zones are relatively close together, you realistically need several days to see all of the sites.
Of greatest importance is arguably the Archaeological Park, an area known to most visitors as Sultanahmet. If possible, allow two days to explore everything this area has to offer. On day one, start with the 6th century Hagia Sophia, followed by the Blue Mosque and the ancient Hippodrome of Constantine. Then, spend the second day at the former residence of the Ottoman sultans, Topkapi Palace, and if time allows, check out the underground Basilica Cistern as well.