Yeah, some of the Greeks, notably the Athenians, were pretty good sailors, but most were just shore huggers.
As far as near neighbors to Europe who were better sailors than them, for the most part: The Phoenicians were one of the great Middle Eastern maritime civilizations, not a European one- they lived in the Western Fertile Crescent region. The kingdom of Punt (in modern day Somalia), the Carians (from Anatolia, super ancient), the Persians, the Carthaginians, etc, etc.
Going a little farther away, the Tamil Chola Dynasty of Southern India could field truly massive fleets during their heyday. As mentioned in the post above, the Chinese were also pretty accomplished sailors- the Chinese Treasure Fleets remain the largest fleets launched by anyone until the heights of the Age of Sail. Japan and Korea also had skilled sailors and large fleets during their heyday.
Cool thanks for the information, got some stuff to look up!
If you're interested, I highly recommend Lincoln Paine's The Sea and Civlization. It's a dense, dry tome, but well worth the read.