I think the best way to do a public dead drop would be to use something that is already there and transfer in a way that looks normal. E.g. giving a certain shop in a mall a modified EC card reader and then have your courier "pay" via NFC.

Ideally you'd like your data transfer to be completely invisible even to watching eyes, ears and attenas, so the best option is to use signals (or the absence of signals) one would expect to be there.