The most important phrase to learn in any language is not 'Where is the library?' which, for years, was the first (and only) phrase Spanish 101 high school students learned.
Instead, one of the most important phrases for tourists will be: Where is the restroom? Naturally, you won't understand the answer if the person doesn't pantomime it, but you can look confused and desperate in hopes that they will show you the way. One additional point here. According to travel-made-simple.com, the best word to use is actually 'toilet,' which is universal.
Next best words all involve courtesy:
Please
Thank you
Excuse me
Hello and polite greetings; the greetings for morning, afternoon, and evening.
I'm sorry.
Finally, you want to learn some words related to safety:
Help!
I am allergic to …
I need (medicine, treatment, police, hospital)
You'll also want to learn the one phrase that will be constantly on your mind: DO YOU SPEAK ENGLISH? Many do, but not everyone. Seasoned travelers say learn the words and try them out and don't let fear stop you.