If it is your first time in Istanbul. You will be surprised when you walk around Ayasofya. Ofcourse you will see lots of "buildings" around from Rome, Byzantiane and Ottomon Empires but dont miss underground sisterns
Not far from Ayasofya (Hagia Sophia), Suleymaniye Mosque is another architectural wonder. Its architect is Mimar Sinan. There is more information about this architect at the following link if you want to discover more. Buildings he designed can be found all around the city varying from large mosques such as Suleymaniye to smaller ones like Kulliye of Valide Sultan.
Hagia Sophia is in the center of that historic peninsula. You can see all the followings in one day (might be quite tiring depending on your fit). Hagia Sophia, Blue Mosque, Topkapi Palace, Yerebatan Cistern, Saint-Irene church, Istanbul Archeology Museum. Don't forget to have lunch at the historic meetball restaurant called Sultanahmet Meetball Restaurant (ask for Sultanahmet Koftecisi when you get there). It's a must have between visits.
Now all this may take one full day depending on your interest level. There are tons of other historic buildings, museums and fabulous monuments in Istanbul. Don't forget to take a Bosphorus tour by the boat as well.