A solar powered computer, something like this: http://juliansarokin.com/how-to-build-a-solar-powered-raspberry-pi/ placed around a city with a wireless network interface setup to use ad-hoc mode such that anyone can walk within its wireless range, connect to the device with their mobile computer phone and exchange files with it.
Assuming you’d have to know of its existence beforehand, one method of doing so is to have a website that displays the locations and also the domain name of the machine so you can browse the files on the device just using a web browser.
There could be a simple upload form to send files from your device to it, with the correct security precautions in place to not allow executing any files.
If these are inside buildings there is no risk of physical damage by people or nature.
Then you’d have an awesome pseudo-sneakernet, filesharing network across a city.