You'll probably be flying into Athens when you go to Greece, so here's a link to the weather today in Athens
The Spring and Fall are my favorite times to go to Greece. It's hot but not unbearably hot like July and August. I don't like riding into a furnace. Winters are cool and wet and it snows sometimes, so that's not the time to go biking there.
GREEK FERRY SCHEDULES
Early Spring and late Fall are the best times to go biking in Greece I've found. However, Ferry schedules must be checked regularly because this is when the ferry times are changing. They're busiest in June, July, August when the holiday tourists are swarming everywhere. If you hate crowds and lineups as much as I do then Spring & Fall are your best choices.
I'm sure you compare fares before you book your flight but I've found that Skyscanner.com is pretty good. Use it to check and compare rates and then book with the airline direct. I've learned that many third party websites that help you book flights are scammers and forums are full of horror stories about good people getting ripped off by these companies. BOOK THROUGH THE AIRLINE YOU'RE FLYING WITH! Then if your flight is rescheduled or cancelled, they'll look after you...third party booking sites will cause you a nightmare if that happens and you'll pay huge penalties after you waste a ton of time getting through to them if you even can.
This small hotel near Athens is great for a base if you want a clean, simple studio close to the ocean and many historical sites. It's well run by a great couple who will go the extra mile to make you feel at home. Chris also likes an occasional beer and knows the lay of the land. He is a walking encyclopedia. It's not expensive and it's even environmentally green. I've stayed here many times and usually end up returning here.
TerraMare Hotelis the best value for money on the island of Kefalonia. This is my favorite Island and this is my favorite place to stay. Nico is the owner of TerraMare and he's a prince of a guy. The facilities include a beautiful swimming pool and a natural Greek setting very close to the town of Lixouri. A ferry goes to Argostoli every half hour.
Many historical sites are closed on Mondays, so be prepared. Due to the economy, some of the smaller ones may not even be open so check before you ride there. When in Athens though, the Archaeological Museum is a must see. Some are amazing and free, especially on the islands. But none are expensive and what a history!
While downtown is the preferred spot to get a hotel in most cities, that's definitely NOT the case here. The downtown or center of Athens, around Omonia Square, isn't a very nice place. Check Trip Advisor Hotels and you'll see reviews for the decent areas. If hostels are your thing, there are nice ones near the Plaka which is the tourist area around the Acropolis. Also, the Backpackers Hostel in Athens is great and location is in the Plaka area.
There are motorcycle and scooter rental agencies in every town and island in Greece. In Athens there are a few agencies but arrange your bike in advance to be sure of availability. I have used MotoRent many times without a problem and highly recommend them.