For an 8-10 day anniversary trip, I know we want to spend a couple days in Athens and spend time in Santorini. My question is - which other island should we visit? I'm debating between Crete, Rhodes, and Mykonos.

Crete, without a doubt.

Another vote for Crete, although I also like Rhodes. I would suggest connecting straight through from Athens to Crete, if possible to maximize your time. Then take the fast boat to Santorini. From Santorini, you either ferry or boat to Athens.

Check out this hotel website in Mykonos google Hotel Tagoo. Its been on my favorites site for awhile as I think it looks lovely. I have been to Mykonos , years ago, and I am planning a return trip one day, and this place looks so romantic, near town , but not in the crazy noisey nightclubby areas, up on a hill , the views,, ahhh. Can't wait.

Assuming your trip is sometime between April and October, Crete and Mykonos both have good connections with Santorini. Knowing the date of your trip, and what your interests are, would help.

Crete anyway. There's nothing on the others you can't get in Crete.

Naxos, if you want to visit an 'almost' real island. It is peaceful and beautiful but with plenty to do and see. I think I got the boat there from Athens and went on to Santorini. The other islands you mention are very, very touristy.

my wife and I did athens and 4 Greek islands 2 years ago. I had a travel agent in Athens book our island hopping. We spent a couple of days in Athens, then flew on Aegean Airlines(a great airline)out of Athens to Hania, Crete. Great spot in western Crete. We were going to take a ferry to Santorini from Herkalion, but our agent didn't like the particular ferry on the day we were leaving. Instead we flew and were in Santorini in 20 minutes. Santorini is a unique island. You have to go there once.
Nick.P.S. If you want the travel company in Athens e-mail and I'll be glad to send you the name and any other information.