I'll just edit my previous post on the subject:
Starting points and ferries:
Island hopping is easiest when you go to chains of islands that are on regular ferry routes (i.e. predictable). You don't have to start in Athens, it is not the only choice by any means.
EasyJet have cheapo (sometimes....) scheduled flights to Athens, Mykonos, Rhodes. These can be used as starting/finishing points. Along with other charter flight destinations like Kefalonia, Zante, Samos, Kos, Santorini.
A couple of easy examples:
1) Athens/Piraeus > Paros > Naxos > Ios > Santorini > Piraeus (you could also take a charter flight to Santorini and do the same thing).
2) Rhodes > Samos > Patmos > Lipsi > Leros > Kalimnos > Kos > Nysiros > Tilos > Symi > Rhodes. In this case ferry/catamarans/hydrofoils are daily and you can just pick a few islands for your 3-4 weeks (You could also take charter flights to Samos or Kos).
The Cyclades island ferry routes are quite complex. 5 main ferry routes and others.
Travelling and Accommodation:
Backpacking in the islands generally speaking the way to go, it's for all ages not just the young ones. Flexibility is the key, easier off the hi-season, and easier to reach the less touristy islands where ferries are not daily and may be at odd hours of the day/night.
Most seasoned Greek island hoppers never book accommodation in advance and travel out of hi-season when accommodation is never full. Room and hotel owners are very flexible about the length of stay and only require 1 day notice of when you are leaving or if you want to stay a few days longer, no problem.
Accommodation is easy to obtain on arrival on most islands, except for mid July/August, the best price is usually obtained by bargaining direct with the hotel/rooms for rent place. On smaller islands there may be no hotels, however there will be 'rooms for rent', signs around the villages. Expect accommodation to be simple and basic, it has improved over the years.
A useful guide book is 'Greek Island Hopping' pub: Thomas Cook. Reasonable island village maps and ferry routes, timetables out of date, but gives you a general view of what to expect.