Jackson International Airport in Port Moresby quickly comes to mind. I did ask why not, and they had a good answer.
"The rascals would back up a truck, with chains, and rip the thing out of the wall, drive into the bush and smash it open. Therefore we have no ATM's in Papua New Guinea".
Quite logical really.
A few others that come to mind. Tabatinga International Airport in the Amazon. Livingstone International Airport in Zambia, Pnomh Penh IA Cambodia, Da Nang IA, Ushuaia IA in Tierra Del Fuego, Vientiane IA in Laos, Maun IA in Botswana, and Mount Pleasant IA on the Falkland Islands I just left certainly had none.
There would be 100s I suspect.
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Glen ~