For me (British English) I would say 'at'. I say 'British English' but I'd go so far as to say it is merely a personal choice rather than a regional choice. Indeed, I doubt it is even a choice, more a matter of 'what comes out at that time'!
You could say 'meet me in the part' means 'inside the park', and 'meet me at the part' means 'outside the park'. If you specified further it would influence which preposition:
"Meet me at the park, just in front of the entrance."
"Meet me in the park, beside the fountain."
Although, I would personally have no qualm hearing "Meet me at the part, beside the fountain", nor, "Meet me in the park, just in front of the entrance."
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