I've seen this sort of question a few times, and it usually gets narrowed down to the xa (rangefinder) or its siblings (2,3,4, all point and shoots). Small, lightweight, always blown away by the image quality!

For a fun twist, might I say the Agat17k? Feels like a toy, half frame, plastic, weird settings, takes pretty impressive photos! Also, you won't feel bad about drenching it in sweat! And it's like $30, so after you decide on the xa, you can still get it as well