Adventurous travelers have a trick to finding a cheap fare: Book a ticket to somewhere, just about anywhere. The airline picks your destination.

Germanwings, a discount European carrier owned by Lufthansa, offers what it calls “blind booking’’ tickets as cheap as €33 ($37) each way. You pick your dates and your interest: party, culture, shopping, sun-and-beach, gay friendly, metropolis or nature. Then Germanwings picks your destination. Once your payment goes through, the confirmation comes with your destination listed. You...