Most visitors to Greece usually dream of island hopping. But with so many islands and with perfectly confusing ferry schedules, it can be a daunting task to put together an itinerary that won't drive you crazy. You can read about ferries in Greece and about the Greek islands, but the reality is that you could be better off not planning every single detail of the trip. You could show up in Piraeus with a backpack, buy a ticket from one of the myriads of vendors at the port, and head for any island. Stay a couple of days and rent a moped to roam around its beaches and towns before you hop on a ferry for another island (make sure the ferry goes to another island and not back in Pireas, and you'll be fine).
While this might sound a bit risky, but the reality is that your chances are good that you'll have a great time no matter what Aegean island you land on. Most islands have plenty of accommodations, and unless it's the middle of August, you'll be greeted by many room owners who will try to entice you to chose their accommodations as soon as you walk off the ferry. Most Aegean sea islands could be comforably visited in two or three days so you will have plenty of time visiting several during a two week visit.
For those who would prefer their travel itinerary a bit more structured, the plan in the above box would give the best sampling of Greek islands at a comfortable pace. All of them are packed tightly in the center of the Aegean (the Cyclades) and ferry connections are plentiful. Ferry connections are the one main thing you have to worry about when you go island hopping since some islands are way off the main ferry lines and don't see any service that would connect them to other islands. You don't have to worry about the Cyclades though. The longest ferry ride would be from Pireas to Santorini. From there, the Ferry rides would be at most two hours (Santorini to Naxos) and at best twenty minutes (Naxos to Paros).
This itinerary is recommended for people who would like to see the most popular islands of Greece and to experience a sampling of quiet time, busy time, white-washed fishing villages, beautiful beaches, and even some very important archaeological sites and museums. If you visit Greece it would be a good idea to experience some of the ancient cultures and every island in this itinerary has plenty to offer. In Santorini don't neglect to visit the bronze age town of Akrotiri that was burried in ash (sort of like Pompeii 1500 years later), take in the spectacular views of Ancient Thera, and spend a few hours in the Museum of Prehistoric Art. In Naxos you can't miss the "Portara" right at the port's entrance, and in Mykonos you can take a boat to the spiritual center of Classcial antiquity: Delos. All that without sacrificing any time away from the sea and sun that you are probably there for.
If you prefer a bit more "partying", Santorini, Paros, and Mykonos are known for their night life, so you won't be deprived of any fun. but for spring break-like fun, substitute Naxos for Ios in this itinerary. Ios is a very picturesque island with beautiful beaches and a reputation for wild, youthful partying. If on the other hand you prefer to stay away from such "party" atmosphere, you can substitude Mykonos for a couple of days in Tinos island (you can stay in Tinos town, or in Pyrgos or Panormos for an even more quiet experience).
Renting a car or a jeep would be highly recommended in all of these islands (after reading the driving in Greece advice) so you can explore some of the more inaccessible places and beaches. All these islands are small enough to explore on a moped or a four-wheeler, but be aware that you have to be extra-extra careful. Many a tourist find their skin scraped on asphalt (or worst) riding such fun vehicles on such beautiful islands.
In terms of a budget, this trip can be done on the cheap, but these are some of the most popular islands in Greece, so in the mid-summer prices tend to go up. To be sure, your biggest expenses would be the ferry tickets. Once there, you can find accommodations that range from a luxurious suite at a hotel with a view, to the rough spot for your sleeping bag in a campground by a beach. Food expenses fall along the same lines. You will find everything, from fancy restaurants to pizza joints, to eating your gyro at the curb. Take a look at the prices, and food in greece
I'd recommend to plan returning to Athens at least two days before your flight out since heavy seas or strikes might preven sailing boats from taking you back to Pireas at the last moment. Not that being stuck on a Greek island would be much of a calamity, but you might have other obligations awaiting your timely return back home.