Corfu is an island so you have to take the ferry to get there. Many car rental companies forbid you taking a car on a ferry. Make sure that you have written permission to take the car on a ferry.
You can spend a whole day in Corinth. There are lots of great sites there. You can visit the canal even take the hike along the top of the canal. You can also visit Ancient Corinth and right beside it the mighty fortress at Acrocorinth. Ancient Nemia is right there as well.
Corinth area sights https://www.flickr.com/photos/stanbr54/albums/72157711755443483
A week is a good time frame to visit the Peloponnese. Be sure to visit Nafplio. It makes a good base to see many of the nearby ancient sites.
Nafplio and Peloponnese http://www.flickr.com/photos/stanbr54/sets/72157632094108982/
Last September we did a week in the Peloponnese and concentrated on the Mani area. Its a great drive. Be sure to plan a visit to Ancient Messene it is a huge site and one of the best in all of Greece. Its near Kalamata. Do plan a day in Mystras it is the last Byzantine city spread out down the side of a mountain.
Here are images of that trip.
For island hopping you could consider just doing Crete. You have sufficient time to do that island fairly well. It has it all. Great beaches, cities with old town areas like Chania which is a walled city with a Venetian era harbour and a maze of back alleys. Rethymnon is similar and Heraklion too.
You will want to visit the famous Minoen site at Knossos and the archeological museum in Heraklion.
South of Heraklion you can visit the ancient Minoen site at Phastos and the fantastic Roman city at Gortyz or Gortyn. There is a buried Roman city in the olive groves there. Bring water there are no services but expect at least 4 hours to explore this amazing site.
Knossos, Phastos and Gortyz https://www.flickr.com/photos/stanbr54/sets/72157645085297380/
After Gortyz you can also slip south to the Libyan sea village of Matala, remember Joni Mitchell and the hippy days. That time is still to be found in Matala.
Lastly you can visit the remote villages along the south coast south of Chania. There are villages down there that are only accessible by ferry,
Ferry trip Libyan Sea https://www.flickr.com/photos/stanbr54/sets/72157653434073393
Crete Libyan Sea villages https://www.flickr.com/photos/stanbr54/sets/72157645487373222/
As I said Crete has it all and I have only suggested you visit the West. You will need another two weeks to visit the east part of the island.
I am assuming you will want to visit Santorini. It is a two hour ferry trip from Heraklion.
Since you are very early in the season I am suggesting you concentrate on Crete because its fairly far south so will be a bit warmer than many of the island chains.