Which airport in Turkey?

Ataturk Airport is much more convenient if you're staying on the European side (if you were staying on the Asia side, I would say Sabiha Gokcen). If you're feeling any guilt about paying for the Turkish Air flight, then take public transit (the tram) to your hotel directly from and to Ataturk Airport instead of a shuttle. You'll save 20 Euros each way and the tram is easy. In the best of all worlds, you can even book a hotel right by the tram (just google it and you'll find the map of the tram system - it's very inexpensive and runs from the airport). I stayed in the Empress Theodora hotel and the tram was literally steps away. The hotel was right by Gulhane Park, Topkapi Palace, and the Archeological Museum.

For me the difference in fare would have to be substantial and cover the difference in transportation costs, the value of my time, etc. If it does, then go for it (you can just stay at a hotel on the Asian side - it's not hard to commute to the Old City by ferry and you'll at least be free of your luggage by then. A lot of people don't see the Asian side at all and I thought it was quite interesting and worth going to).

I agree with everything Agnes wrote. Yes, money counts, but time and hassle count too.

I found the Turkey Travel Planner website very helpful for my trip. Here's his page on getting in from Sabiha Gökçen Airport: http://www.turkeytravelplanner.com/go/Istanbul/Transport/s_gokcen_transport.html

And from Atatürk Airport: http://www.turkeytravelplanner.com/go/Istanbul/Transport/gokcen2ataturk.html

An even simpler answer is to approach this as a math problem. If your round-trip transport shuttle costs for Sabiha Gokcen are 60 * 2 = 120 Euros versus the round-trip transport costs for Ataturk 20* 2 = 40 Euros, the difference of 80 Euros exceeds the $80 difference for the Pegasus flight by a very small margin (about $7 given today's exchange rate). This assumes that you're staying at your chosen hotel in either case. So it doesn't seem like a winning strategy to land at an airport that poses more time in transit to your hotel without a sufficient financial benefit. Of course there are a host of other variables you can play with and see what the total costs between Option A and Option B are. As long as you are tram accessible, the transportation costs are largely just in terms of your time since the tram is very inexpensive compared to shuttles or taxis.

Pay the €20 for the hotel shuttle or arrange a different one on your own. To get there from the airport by tram, you have to change trains - and probably up and down a flight of stairs - to get to the other track. Then you have to find your way from the tram stop to the hotel. Not worth the trouble.

Take Ataturk Airport, get off plane, go to Floor -3 and take Metro(M1A) to city. Drop off in Zeytinburnu station from M1A and get on T1. It will take you heart of Old city, Sultanahment etc.. or you can take only M1A to last stop which is Yenikapi and you can walk to Sultanahmet (about 3km) or you can take it and get off in Aksaray station and you can walk to Sultanahmed (about 2km)
It will cost you about 8 TLand it wont take no more than 70 min to arrive there by this option. A lot of tourists do it!
Good luck