The most recent xkcd:

For me, at least, it should be "closer to", not "closer of". This isn't a necessary truth: "I can't get within 500 yards of you" would be perfectly fine; and in French, for example, the preposition used with "plus proche" is de, not à:
Tout ce qui est plus proche que 3 mètres ou plus éloigné que 5 mètres de vos yeux est flou.
C'est une saveur qui est plus proche du thym que de l'anis.
But in English, it seems to me, close and most of its synonyms — without or without -er and -est — should take to. Walt Whitman wrote "Come closer to me", not "Come closer of me". The old song is "Nearer, my God, to thee", not "Nearer, my God, of thee". There are more recent songs "Closer to you" and "Close to you"; as well as "Closer to me" and "Close to me". But the only pop resonance for "closer of you/me" seems to be a non-native-speaker's translation of "Un poco cerca de mi".
It's possible that Randall Munroe originally wrote, or at least thought, "I can't get within 500 yards of you", and then changed "within 500 yards" to "closer than 500 yards" without changing the preposition.
But it's also possible that this is one of the many points on which different speakers of English have different ideas.
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