Where is the best place to exchange US dollars into Turkish lira after arrival there? At the airport, the hotel, exchange booths in the city, or the banks?
None of the above. Don't exchange currencies unless you want to pay through the nose. It costs at least 20% above the interbank exchange rate for you to obatain cash that way. If you want some lira in your pocket on arrival, you can try a large bank here in the US or someone like AAA. You'll pay around 10% premium to do that, so only exchange a couple hundred dollars. Otherwise, just use an ATM in Turkey just like you do at home. Notify your bank of your travels. Depending on your bank's fees, you'll pay between 1-4% above the rate for using an ATM.
When I travel to Asia (Thailand, Malaysia, Singapore, etc.) I always find the best rates at currency exchange booths in town - sometimes at the local banks. The airport was always a bit higher and the hotels were never competitive but handy when you needed cash late at night. I'm surprised to learn that exchange booths and banks in Turkey would charge 20% above the official rate.
There is a row of about 4 or 5 ATM's in the Istanbul Ataturk Airport, right on your way out, so it's very easy to get local currency upon arrival. Once you're in Istanbul itself, ATM's are as prevalent as in any large city, i.e., they're everywhere. Douglas is right (well, I can't confirm his percentages, but the concepts are correct). ATM's have the best rates for foreign currency, even counting the fees (and there are ways to minimize those, if the fees from your current bank are too high). When you exchange cash, wherever you do it, you don't get the "million dollar rate" - the exchange rate used by banks for huge transactions. But credit and ATM card transactions do use this rate, plus, of course, a small markup so they make a profit. You still come out ahead. As said, if you want to arrive with some Turkish cash, you can, but after that, stick to ATM's. Here's Rick Steves's excellent tips about using ATM's. Be sure to read the linked pages, like Cash and Currency Tips, as well: http://www.ricksteves.com/plan/tips/cash-machine-atm-tips.htm
Thank you gentlemen, this is very helpful. One technical point: I checked the exchange rate for today between USD & Turkish lira and it was around 1.795. So I asked the owner of the hotel we'll be staying at, how much the exchange booths (which she recommended as giving the best rates) are charging today and she said, 1.8. I suspect their margins are fairly competitive. At any rate, I'll definitley use the ATM at least once to compare and report back. We'll be in Turkey on March 16-24.
I used the ATM at Ataturk Aiport to get initial funds. I also got smaller coins right at the airport (I think it was a machine that you can stick a bill into and coins spit out) to use their tram system into Sultanahmet right from the airport.