So how is it that the ancient Greeks managed to better insulate their Olympics from geo-politics? The answer is that they didn't move the venue every four years the way we do. Instead, with one exception, they always held the contests at the religious sanctuary of Olympia, in a politically irrelevant corner of the Peloponnese. Perrottet suggests that we follow the Greek's example and find a permanent home for the games in some safe little neutral country like Liechtenstein.
Of course, as the Greeks were nearly constantly at war with each other they had significantly more incentive to hold the games in a neutral location. Our problem is mainly that we don't see a tyrannical form of government as a disqualification for hosting the games, but we could avoid offending the tender sensibilities of the world's dictatorships by holding the games in the same place every four years.