Olive Oil

That’s a personal preference question with no correct answer. If you’re there maybe ask a local what some of the better brands are since there definitely is a difference. Where you’re at in the country will also make a difference as there may be some local producers that might only sell in local markets.

If you’re from the U.S., getting it back may present its own set of issues.

It's hard to say what's best. In Corfu, the Governor is considered the best due to its high antioxidant levels. However, you cannot cook with it and it tastes peppery.

Just taste lots. Best is very subjective, and really depends not only on personal preference, but what you plan to do with it. An oil for salads can be different from an oil for drizzling, for bread, for things like dips, and definitely different for cooking.

Probably best would be to find a small local producer in a town you will be, if you like it, get it. Apart from the taste, the personal connection to the oil will provide more flavor to the mind, than actual flavor in the oil. Buying something in a grocery store or market, without knowing its origin, won't be the same.