This would be great if you wanted to talk to yourself without anyone understanding what you’re saying, for example, or if you didn’t want anybody to know what you were writing down. It might also be useful if you enjoy lots of foreign language media (see music, tv shows, movies) and want to experience the “original” rather than through dubs and subs.
Personally, I would go for either Russian or Estonian, both of which are because I frequently listen to lots of music that are in those languages, and they aren’t spoken by any of my friends.
“Region” would have to be extremely small around here to not include someone who speaks almost any (natural) language a typical person could think of.
I’ll just go ahead and answer a different question: If I could instantly learn any language and my SO could instantly learn it also, I’d pick ASL, because it would be very nice to have a way to communicate that works where talking either doesn’t work (loud places, for example) or would disturb others, or just across a large room.
Oh, sign language could be a good one!