3 weeks in Greece

I would say with 3 weeks to do it in, you probably could do about 5 islands (not 6) plus Athens if you're young and flexible, willing to travel at night sometimes. Our advice would differ a great deal depending on WHEN you plan to go... PLEASE share your exact dates of Athens arrival/departure.

In general if your dates are in August, the islands you mention will be absolutely HEAVING with holiday-makers, not a single metre of sand to spread your beach towel on, and all ferries busses jammed as well. Crete would be the exception simply because it is so large that you can escape the crowds. You may have to look at some less-visited islands, if you want more breathing room ... I have some delightful ones to suggest if you'll just share a bit more.

Another consideration is BUDGET. You have selected (aside from Crete) the MOST touristic islands, thus the most expensive. What is your Euro budget per day for EVERYTHING (lodging, food, drink, transport, misc).

It also always helps if you can give an idea of your interests. Is it mainly for beach and sunshine, with a bit of nightlife? Or are you into ruins and history, do you like hiking, are you interested in small villages where you can encounter authentic Greek life a bit.? What are your priorities.

I highly recommend touring the Peleponnese. It's beautful, filled with ancient wonders and an entire different culture than the islands. We took the local train from Athens to Corinthos and picked up our rental car there. Then visited the ruins of Corinthos. We drove 1/2 way across the Peleponnese through the gorgeous mountains filled with wildflowers to a tiny hilltown called Dimitsana. It was magnificent. We stayed in a 15th century B&B which was beautiful. We drove to Olympia one day from there and toured about. This was an easy daytrip from Dimitsana. Then we drove all the way south east to Napflion, which is a beautiful, bustling tourist town with a great Venetian castle way up on the mountain top. It also has a little one in the bay and bits of a Roman castle. It has great B&Bs & bars & restaurants. From there it was an easy daytrip to Mycenae, Epidavros & Tiryns plus others. The Venetian castle in Napflion is also worth a visit and has spectacular views. You could do this a bit in reverse and start down south, go to the middle and then to Olympia & on to the west coast for a ferry to Corfu. There are ferries to Santorini, Mykonos & Crete from Piraeus but this requires going all the way back to the east coast so perhaps you should go to those islands first.

The suggestions given regarding the Peloponnese is good. I would avoid Zakynthos unless you want to be with a lot of rowdy English and Germans crowded on a beach that should be off limits because of the sea turtles who would like to nest there but are being driven away into extinction.
Corfu is another place that has been totally taken over by the English and German tourists. Not much left of Greece there.
Crete is the best place you have mentioned.
You don't give enough information about your likes and dislikes-what you enjoy doing. If you are young and want beaches and bars then all those islands will suit you.
If you want to see something of Greece that is off the normal tourist beat then you need to stay inland. Particularly in the northern part where few tourists go.