Akrotiri is a "Sovereign Base Areas Overseas Territory of the United Kingdom", situated on the island of Cyprus. I don't class this as a "proper" country, but the Travelers' Century Club does. But I guess that if I'm counting the UN buildings in Geneva and New York, then I should be counting this one.
While I was on Cyprus I travelled through Akrotiri several times.
Hmmm, I've visited a couple of American Airforce bases in the UK, I wonder if they count??