I always try to learn the local language- have done pretty well with the Indo-European branch (French, German, Italian, Spanish, Russian and now Greek) because they're related but have given up on Hindi and Hungarian. OK, maybe Hindi IS Indo-European but I still gave up.

Do your best- the locals almost always appreciate it and you pick up nuances you wouldn't have if you were oblivious (news headlines, concert notices, menu items, etc.) But you could bluff your way through most of the major cities in Europe with only English.