I'll be in transit in Istanbul (Turkey) for 13 hours next month. How should I kill my time? What shall I see?

I honestly know nothing of the country. I'd like to see a bit of the city before I come back home...
Answers

Robsteriark

Take a taxi to the Blue Mosque and the Agios Sophia which faces it. There’s also the Hippodrome (ancient Roman race track remains) right next to the Blue Mosque. 13 hours really won’t allow you time to do justice to the Topkapi Palace though. Blue Mosque is free entry as is the Hippodrome which is a public space. Agios Sophia is not free and can have long entry queues, but just seeing it even from the outside is amazing. Istanbul is a fabulous city and you could easily spend a week there and still want to return and see more. Eating and drinking is very cheap. Ask at the airport information desk what a taxi fare to and from the airport should usually be: some taxi drivers will take the piss and overcharge, a few will claim you gave them a 5€ note instead of a 20€ note so be very clear to tell them “Here’s a 20€ note” as you pay them. Most drivers are scrupulously honest though. If you like beer, make sure to try Efes Dark. It’s lovely!

Bill-M

Blue Mosque and the Agios Sophia and the Market Place. They are all close to one another.

Siddhartha

Ataturk museum.