To make a tour to the mainland of Greece I would suggest you to rent a car. It's the easiest and nicer way to explore places like Peloponissos and visit the best known archeological sites, like Delphi, Olympia, Mycanae, Epidaurus...driving in Greece is not difficult if you have a good map.

As for the islands, you can go by ship or plane. If you need my personal opinion, a very nice trip is to Rhodes by plane and then visit the small close islands, like Symi, by boat.

If you would like to go to Crete, you also need to rent a car, because Crete is a very big island and you need more than a month to make a full tour of it.

Regards, Joanna in Athens