1. I’ve lived and worked on Rhodes, and although it is a bit far away, I agree that it’s a great island. If we’re talking about departing from Athens, taking a ferry takes quite a long time (15-18 hours, sometimes more) but costs approximately 40 euros. Many people fly to save time; takes 1.5 hours and costs approximately 100 euros.

Personally, I love Crete because it’s a big island rich with different cultures (lots of countries invaded and left behind their influences), interesting sites, specialty local food and beautiful beaches, plus some gorges you can hike and nice people.

To sail, there is one ferry that takes you from Rhodes Town to Sitia, Crete three times a week and costs 25 euros.

To fly, both airlines currently take you back to Athens: Rhodes-Athens-Irakleio/Chania. This may or may not change in summertime (schedules change with the season and are announced accordingly). Costs approximately 100 euros.

Karpathos is quite close and easily reached by ferry. Symi, as another respondent said, is also quite nice. Kos is a bit touristy, however if you go to a less-traveled part of the island, you can find what you’re looking for quite easily. Since everyone’s tastes are different, may I recommend you visit a bookstore and thumb through a few travel guides and see what they say, then perhaps see what best suits what you’re looking for?

2. Island hopping is not as cheap as it used to be. Fares and hotels have gone up steadily, and anyone not using the euro (Canadians, Americans, Australians) find the exchange rate is not in their favor. So it depends on which currency you’re using and your definition of expensive.

3. As I said previously, schedules for ferries and flights for the season are announced accordingly, so they change. You would be able to pre-book, however don’t be surprised if your scheduled times are changed or re-scheduled. Most people just go to the port, inquire, buy a ticket and hop on.

I don’t know many people who use the term “island hopping” anymore, but it refers to the fact people purchase a ticket and hop on the ferry, then hop off wherever they choose, then hop back on and then off. Nowadays, they book tickets without an open schedule, and your time/destination must be stated and paid for in advance.

Ferries from Rhodes go to:

Astypalea
Halki
Kalymnos
Karpathos
Kasos
Kastellorizo
Kos
Leros
Nisyros
Patmos
Pireaus (Athens)
Sitia (Crete)
Symi
Tilos

Any travel agency would be able to assist you if you need it, and most have travel packages, though some may not be customized.

Whatever you decide to do, have a great trip!

to island hop, you would take ferries, its easier. And from Rhodes, the perfect island to island hop to is Symi, its a beautiful island only 45 minutes away by the hydrofoil or jetcat ferries. There are festivals here throughout July and August and Breathtaking beaches. The islands surrounding Rhodes that are close-ish are
Tilos — never been, sure its nice, but very small, only a few hundred ppl
Kos — never been, but heard its great, has its own airport so it must have alot to see and do.

You could easily do that because most islands are interconnected. So once there you can get the ferry going on the next island.
Suggestion #1: Syros.Tenos, Mykonos. Departing from Rafina, or Piraeus.
Suggestion #2 : Santorini, Crete, Rhodes, Kos. departing from Piraeus.
The combinations are limitless, if time and money are not the problem.
One more closer to Athens is the visit of the islands of Egina, Poros, Idra, Spetses. Hydrofoils (dolphins) departing from Piraeus,Pasalimani.
Check the following to get more ideas.