About 80% of the time I land in a foreign country with 0 local currency. I use an ATM at the airport, although I do this less and less because of unfavorable exchange rates. I just get myself to the city and use a regular ATM. If I need cash to get to the city center, I don't take out much more than what I need.
Assuming you don't allow the ATM to do the conversion, isn't the exchange rate determined by your bank? I've always used airport ATMs too and the rate has always been near market.
In some airports, LHR is one, the ATMs have been taken over by currency exchange (even the unbranded ones) and won't give you a choice of conversion. My husband pointed it out a couple of years ago; when I calculated the exchange rate, it was atrocious!
London is easy. I either have a car waiting, use my phone to get on the tube, or charge a heathrow express ticket to a credit card. Heck, I've gone 2 weeks in London without using cash.
In comparison, I definitely needed kuna in Croatia (I paid for everything in cash), but the ATMs, at least in Zagreb -- even in bus and train terminals -- added absolutely no fees and the exchange rate was the bank rate. Split & Dubrovnik were another matter.
In Cambodia, when I traveled there well over a decade ago, crisp US dollars seemed the preferred currency. But it had to be new/crisp bills. During a bus stop I had to plead with the street vendor to take a worn dollar when I didn't have enough riel. No credit card or bank would have helped there.
This is really good to know. I might have called for an unbranded ATM that didn't offer a choice. Do they at least tell you that they're doing the conversion?