What is the best of Istanbul?

Istanbul is full of great attractions. In the old town I would add the Basilica Cistern, a stop in on of the Hamams like Cağaloğlu Hamamı Sk and Sefa Restoran for a fantastic lunch. Dine at the Seven Hills for stunning views of the city.

On your way to the ferries book a ticket at Hodjapasha Dance Theater to see the Dervish dancers and walk through the Gulhane Park to get some Turkish tea in their café. Go to the New Mosque and afterwards grab a fish sandwich form the boat stalls in Eminonu Bazaar where the ferries are.

Far removed from tourist areas you can go Vefa Bozacısı to get  Boza, an Ottoman-era drink and Pomegranate vinegar cream. Right around the corner from Vefa you can climb a ladder (literally two guys with a ladder) to walk on top of the Valens Aqueductand get the most amazing views of the city and the Bosphorus. Climb down and go to GÜL BÜRYAN KEBAP SALONUor any other kebab restaurant in this "meat-packing-district" street.
Enjoy!

This a very broad question but places like Dolmabahçe Palace Topkapi Palace Blue Mosque Hagia Sophia Galata Tower are all world class attraction and this is just to mention some of tem as Istanbul really has a lot to offer.

Grand Bazaar and Spice Bazaar are also very interesting to visit as long as you can accept a lot of hustle and bustle.

And Bosphorus Cruise | Day Cruises | Istanbul Sightseeing is also well worth doing.