It’s best to visit Greek islands within the same group. For example, I wouldn’t recommend visiting Corfu and Santorini on the same trip as they’re on opposite sides of the country. Instead, visit islands in the same island group: the Cyclades, the Sporades, the Dodecanese, the Ionian, the Saronic, and the Northeastern Aegean. For one, they’re close to each other. And two, they have frequent ferry connections with each other. For first time visitors to Greece, the Cyclades make the most natural and convenient introduction.
Can you see all the major sights in Athens in one day? No. But you can see the Acropolis, Acropolis Museum, and the top historical sites of the Plaka in one day. If you had an extra half-day then visit the Archaeological Museum in Exarcheia. That still leaves many great sights but you will have seen all of the iconic Athens attractions. Adding Naxos is always a good idea. You might even enjoy it more than Mykonos (but no nightlife like Mykonos).
Ferries are not really cheap any more – certainly not like they used to be – but the vessel fleet is better, safer and faster than in previous years so the cost is justified. You can get exceptionally cheap deals on longer-haul routes if you are prepared to forego a booked seat: €14 v €40 on a run to a mid-distant island, but it’s probably wise to consider taking fast catamarans to get to core islands (Mykonos, Santorini, Paros etc.) and even then, go the extra 10/15% for Business or even VIP class for the extra comfort. On longer hauls it can be cheaper to fly if you seek out flights online and book beforehand.
In the 1990s, "open skies" agreements became more common. These agreements take many of these regulatory powers from state governments and open up international routes to further competition. Open skies agreements have met some criticism, particularly within the European Union, whose airlines would be at a comparative disadvantage with the United States' because of cabotage restrictions.
Moreover, the industry is structured so that airlines often act as tax collectors. Airline fuel is untaxed because of a series of treaties existing between countries. Ticket prices include a number of fees, taxes and surcharges beyond the control of airlines. Airlines are also responsible for enforcing government regulations. If airlines carry passengers without proper documentation on an international flight, they are responsible for returning them back to the original country.