Where to live

Downtown Istanbul is basically divided in three parts, because of the rivers. In the East, there is Sultanahmet which is the historical quarter; in the North, there is Beyoğlu with the famous Taksim Square; and in the West, on the Asian side, there is Kadıköy.

Kadıköy is a great place to be, with lots of restaurants and bars and way less touristy than the other neighborhoods. And it also costs way cheaper on Airbnb!

Transportation stays easy thanks to all the available boats at the Kadıköy pier (e.g. every 20 minutes to Eminonü/Sultanahmet).

Where to eat

Where to have a drink

What to do during the day

Should I even mention the classics? Hagia Sophia, Blue Mosque, Basilica Cistern and Topkapı Palace in the Sultanahmet quarter, Taksim Square in Beyoğlu.

Less classic things (although still quite touristy of course):

Misc

You definitely want to buy a Istanbulkart for transportation. It is around 10 TL and will greatly facilitates your trips throughout the city (and will even allow you to use public restrooms!)

Do not go to western-like malls in Istanbul, it is really not worth wasting your time. The prices are the same as in France, in my case, and the stores are exactly the same as well.