Holy Ramadan is coming to all Muslim community. It starts at 21. August 2009 and ends at 22. September of 2009.
These days are best days for visiting istanbul. Sultanahmet is like open air food bazaar you can find everything inside that bazaar and cheap. Day time noone eats anything but evening time all people are in Sultanahmet having fun.
My point is if you want to visit istanbul come to istanbul in ramadan and live the real holy spirit of ramadan see people how connected to each other and see how rich peoples helps to poor ones. 

Sultanahmet square is very important place in istanbul. It is knows as Hippordrome which was a horse racing track in old Istanbul. Today this square called Sultan Ahmet Square.
In that place you can see,

• Serpent Column

To raise the image of his new capital, Constantine and his successors, especially Theodosius the Great, brought works of art from all over the empire to adorn it. The monuments were set up in the middle of the Hippodrome, the spina. Among these was the Tripod of Plataea, now known as the Serpent Column, cast to celebrate the victory of the Greeks over the Persians during the Persian Wars in the 5th century BC. Constantine ordered the Tripod to be moved from the Temple of Apollo at Delphi, and set in middle of the Hippodrome. The top was adorned with a golden bowl supported by three serpent heads. The bowl was destroyed or stolen during the Fourth Crusade. The serpent heads were destroyed as late as the end of the 17th Century, as many Ottoman miniatures show they were intact in the early centuries following the Turkish conquest of the city.[3] Parts of the heads were recovered and are displayed at the Istanbul Archaeology Museum. All that remains of the Delphi Tripod today is the base, known as the "Serpentine Column".

• Obelisk of Thutmose III

Another emperor to adorn the Hippodrome was Theodosius the Great, who in 390[4] brought an obelisk from Egypt and erected it inside the racing track. Carved from pink granite, it was originally erected at the Temple of Karnak in Luxor during the reign of Tuthmosis III in about 1490 BC. Theodosius had the obelisk cut into three pieces and brought to Constantinople. Only the top section survives, and it stands today where Theodosius placed it, on a marble pedestal. The obelisk has survived nearly 3,500 years in astonishingly good condition.

• Walled Obelisk

In the 10th century the Emperor Constantine Porphyrogenitus built another obelisk at the other end of the Hippodrome. It was originally covered with gilded bronze plaques, but they were sacked by Latin troops in the Fourth Crusade. The stone core of this monument also survives, known as the Walled Obelisk.

• Statues of Porphyrios

Seven statues were erected on the Spina of the Hippodrome in honour of Porphyrios, a legendary charioteer in his time who raced for the two parties which were called "Greens" and "Blues". None of these statues have survived. Only the bases of two of them have survived and are displayed in the Istanbul Archaeological Museum.

Istanbul is 1,830.92 km2 and has different streets, ways, roads, buildings etc. 
I advice you google as a map and giving you the link which you can find everything inside.
Here is one map too you can print it or email it to a friend. Have a nice holiday.

• See Egyptian Bazaar (Misir Carsisi) and buy your self mixed herbs and spices
• Walk to Grand Bazaar (Kapali Carsi) to see tons of jewellry, diamonds, watches carpet, leather 
• Take a look to Turkish Bath (Cemberlitas Hamami) and try to have a bath in our hamam. You will reborn.
• Walk to Sultanahmet see Topkapi Palace, Ayasofya, Blue Mosque, Horse Square and all beauties. Be sure to sit on a open air cafe and drink Turkish tea.
• Take your bag and walk down the Sultanahmet passing through Gulhane Park to Eminonu and enjoy all whole salers in Tahtakale.
• If you are not tired go to Galata Tower to see istanbul bird view.