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Note: I created this wikipost using info from the thread. Some of the info may be out of date, so please update the wiki if you have new information.

No airport, and no airport nearby:

Andorra
Pitcairn Islands (British Overseas Territory)
Saint Helena (airport under construction)
Tristan da Cunha (British Overseas Territory)
South Georgia and the South Sandwich Islands (British Overseas Territory)
Tokelau (New Zealand)

No airport, but airport nearby:

San Marino
Vatican City
Liechtenstein
Monaco

Has airport, but unreachable on Miles:

Somalia (Kenya used to fly to Hargeisa but no longer)
Nauru
Tuvalu
Antarctica (some airports but no commercial flights)
Ascension Island (British Overseas Territory)
Greenland