Unless you already have a kick ass social life (hanging out with your mates in a bar or at a soccer/football match doesn't count): learn Argentine/Rioplatense Tango. It's the hardest couple dance and best suited for engineers -- for many reasons. If ballet is the assembly language of dances, tango is C. ;) AMA. :]

TLDR; I would give an eye or a hand if someone had given me this advice when I was 20.