I'm citizen of Uzbekistan, and I don't need visa for Turkey. And I'm flying transit 13 hours, can I go outside the airport for sometimes, holding my transit ticket?
Simple answer, Yes you can. Just make sure you get back to the airport before the flight. If your flight is in one ticket, then you do not even need to pick up luggage and re-check it in (thanks to @jpatokal for the reminder). Just go out, enjoy your time :)