Actually I think both of these are fine and there isn't a rule about the order they should come in. However, it sounds more natural and (subjectively) nicer if you group the phrases which are relevant to each other. For example, "as a kid" and "in the early 50s" both refer to the timing, and it makes sense to group them together, and not split them up with "at XYZ place" (which is giving spatial rather than temporal information).
So any order is fine, but I would suggest
As a kid in the early 50s, at XYZ place, I saw ABC.