I, too, have a Raspberry Pi 1! They are incredibly slow and don't have wifi, unfortunately. I've been searching for a project for mine for a while, but haven't found anything that appeals to me. Basically anything that is text-heavy would be ideal, since anything with video is too much for this thing. That said, I did manage to set it up ages ago with RetroPie, and found that it can emulate NES, Gameboy and older games, while SNES games are too much for it.
With that in mind, I've considered hosting a Calibre server, basically a book server, but haven't taken the plunge yet. A few other ideas I've had are a GUI-less programing computer/hacking device, music player, or eReader.
Offpunk is a command-line web browser that can handle several protocols and pulls sites down for archiving. It would probably be fairly simple to put together a PC for archived websites and texts. You could grab Wikipedia and Project Gutenberg (provided you have enough space), and sort of make an end-of-the-world offline reference device. Similar to those
vape-powered webservers, you could also probably serve up a simple website (nothing too fancy or heavy on the scripts!)
I'd be interested to see what other ideas there are out there. I'm sure someone's come up with better ones than me.