How many days?
Istanbul is a cartographical labyrinth with sights and experiences awaiting you round every corner. How long to stay depends on how immersed you want to get, but a week should be enough to cover the most famous attractions.
How to get from the airport to the city?
Havataş Shuttle Buses are available from outside the terminal and leave every half an hour for Taksim between 4:00AM and 1:00AM. Taking a taxi is, however, the most convenient way, and shouldn't be more expensive than the shuttle service between a group of four. Be sure to ignore the hustlers inside the airport and take an official vehicle from the taxi rank at the terminal exit.
Where to stay?
The key touristic areas are Fatih and Taksim, and which to stay in depends on the nature of your stay. Fatih is the old town and home to many of Istanbul's historic landmarks. Taksim, on the other hand, is modern and appeals more to those visiting the city to shop, dine, and party. Traveling between the two is simple, so don't worry if you fancy hitting the dancefloors after the Hagia Sophia!