I have read many times that early Mediterranean seagoers (as well as those during later ages) hugged the coast and feared the open sea due to storms. However, how does this fit into voyages between Greece and Egypt? Did ships always go the very long way around? What about the Egyptian campaign in ~460BC? Didn't the Athenian fleet go directly from Cyprus to Egypt, as this wikipedia map would suggest?
They did actually! Ancient seamen were much more impressive than we usually give them credit for. After all, the technology that built Roman galleys was really not all that different from the technology the Norse used to build ships, and they got as far as Greenland or possibly even America! Ancient sailors preferred to stay closer to the coast much like modern ships still prefer to stay within reach of land, it's just safer. However, the idea that they never went out further from the coast came mostly from the lack of shipwrecks found in deeper water, with the vast majority of ancient shipwrecks coming from 30-40m below the surface.
That, though, is easily attributed to the simple fact that it's really hard to look for shipwrecks in deep, dark water. Sediment settles thicker in the calmer, deeper waters, burying a great deal of shipwrecks. However, modern technology has been able to unearth a number of very deep shipwrecks from the Greek/Roman period. Exactly how widespread long distance travel by deeper routes was is up for debate (again, lack of all that much evidence), but new shipwrecks have been discovered over a mile deep in the Mediterranean, proving that it did happen to some extent.
Sources: http://en.wikipedia.org/wiki/Ancient_Black_Sea_shipwrecks http://www.nbcnews.com/id/47605902/ns/technology_and_science-science/t/roman-shipwrecks-found-nearly-mile-deep/#.Uv2HjEJdX_M http://press.princeton.edu/chapters/i8694.pdf
Athens at its height, in the mid to late fifth century BC, had some 400 triremes. There were standard routes that were taken, depending on where the ships were headed.
Two techniques were used; namely, hugging the coasts, and island hopping.
Regarding the campaigns in Egypt, the map you linked is probably the route that was taken. What the map fails to show are the large amounts of islands that chain the Piraeus to Cyprus.
Long expeditions (and even short ones) could be very hazardous, and it was always best to stay along the coasts, and taking short-cuts by island hopping, when possible.
When sailing to Sicily, the longest route was the way to go. The Athenians sailed from the Piraeus, and along the Peloponnese, eventually going north riding the east coast of the Peloponnese.
Then continuing north, they would have stayed relatively close to shore heading towards Northern Greece. They would dock on the island of Corcyra, (in northern Greece) and from there sail in a straight line to the coast of Iapygia (the heel of Italy's boot). This was likely one of the longest stretches without a coast (some 100 plus miles), right through the Ionian gulf.
Then it was just a matter of hugging the coast of southern Italy, reach the tip, which was Rhegium, and boom, you're in Sicily!
As a follow up, how long could, for instance a greek trireme, stay at see before it needed to return to land to resupply? How far could they conceivably travel before needing to make land fall?
