Gibraltar airport is actually an RAF station though civil flights can use it, but there are all sorts of airspace issues with Spain. Flights are not allowed in morning and afternoon rush hour because of the affect on traffic! Was working there once when one of the barriers failed, so the road had to be blocked off with station vehicles!
Anyway, enough reminiscing. I'll point out the South Atlantic islands like St Helena (not flat enough), South Georgia and Sao Paulo - though not sure if any of them can be classed as 'politically independent'!
Are there any of the states of the UAE without one? And what about Bhutan?