Boom, you can throw it anywhere in a neighborhood or apartment building and access it from the cloud. You could leave one behind at each stop when traveling to get a distributed network solution.
It's still a solution in search of a use case...though they could be used as TOR exit nodes.
Then, charging, you'd want at a bare minimum, a 10Watt solar panel. That, at an average of 6 hours usable sunlight each day, could possibly keep you running. Get a few dark stormy days though, and you'd run out of juice I think.
Could be fun. I'm tempted to co-host my Pi in Austria now that I'm looking at using Arduinos for my project instead. (Order of magnitude less current drain and instant start, which is awesome)
I do this currently with a raspberry pi in the front of my backpack, using a 4500mAH lithium ion battery I bought off Amazon. Works great. It gets about a 12 hour charge so far, but I haven't really been keeping careful track of battery life.
I "know a guy" who will recharge it for you.