Shaner - I was in Greece - once! I didn't really have an issue with having people understand me - but many Greeks do speak some Italian - as do I. Sign language helps.
Learning the Greek alphabet might help.
The problem though will be when you say something in Greek and do not understand the reply.
Idiom is an issue.
I also cannot speak dialect. I was taught some Italian by a woman who moved to Toronto from Milan who did not speak dialect. I had no idea what my Italian hairdresser was saying to me when he spoke in his native dialect.
If you can lay your hands on a basic textbook that should help you.
You will see many people who appear to be English or Irish - but they cannot speak a word of English!
We ate where the Italians ate - and just ordered what they did.