Until recently I only knew that Turkish airlines, Qatar airways and Emirates offer the tour for transit passengers in Istanbul, Doha and Dubai. A few days ago I found out that Thai airways and Singapore airlines offer the tours for Bangkok and Singapore. We did Istanbul stopover tour twice, in December 2014 and March 2016; both times with our daughter (seven-month old the first time around and 23-month now the second time). We did two different tours with different destinations because they have several different schedules depending which day your transit its. You can find the detail on their website, but in short, they have three different departures depending when your transit is, with three different tour lengths depending when your connecting flight will be departing; but your transit has to last for a minimum of six hours. It looks more or less like this: you land in Istanbul, get your visa (if you need one) and pass immigration, find the counter and register yourself for the tour, wait for the departure and gather with other participants, and a tour guide will pick you up. They provide a bus which picks you up at the airport, and first drive you to have breakfast (for morning departure). After breakfast you do a walking tour to visit major touristic destinations in Istanbul (first time around they took us to the Blue Mosque, Hagia Sophia and Basilica Cistern, the second time around they took us to Basilica Cistern and Topkapi palace) and give you free tickets to enter these places. In the end, they took you to have lunch and the bus drive you back to the airport. All for free. If you have a longer transit time, take a 12-hour tour, and they have another schedule for you after lunch. We had a connecting flight at 5pm so we did the half day tour.
Next time we go to Indonesia (which probably will be the beginning of 2017), we're planning to fly Qatar airways which also now fly from Zagreb, and take their free Doha tour. With Turkish airlines you have to pay for your own visa (it cost around EUR 25), while Qatar gives free complimentary visa. If you're a solo-traveler and not a fan of organized tours, just agree with the tour guide after the bus stops in the city that you'll go see around by yourself and be on the bus at the agreed time for departure. If you're traveling with a child like us, it's probably easier just to go with the rundown. The thing is, both times we did the tour, no other child was present. In a group of around forty of us, my toddler was always the only child (which made her the star of the tour). Most family prefer to just stay in the airport (in their safe zone) waiting for the next flight, rather than going out, back in, doing all the hassle. And I want to reassure you why we think it's pretty cool to do the tour with a child (or two):