We were in Greece for 2.5 weeks in May. We visited Santorini, Naxos, Nafplio and Athens. For Santorini, I highly recommend renting a car for a day and driving around the island. The caldera views are stunning but we also really enjoyed our day traveling around the island. We visited the archaeological site of Akrotiri, the Akrotiri lighthouse, Red Beach, and the Black Sand Beach at Perissa.
While in Nafplio, in addition to visiting Mycenae and Epidaurus, we also visited the Byzantine ruins of Mystras, which is one of the highlights for me. It is absolutely stunning! It's a one hour and 45 minute drive from Nafplio to Mystras, but it's well worth it.
Also while in Nafplio, we drove down the Argolis Peninsula to the small resort town of Porto Heli and then on to Ermioni. Both places are lovely. We went for a quick swim at Porto Heli and then had dinner at a fish taverna in Ermioni on the water. Our meal was mediocre but there are quite a few restaurants on the harbor to choose from.
I was on Hydra and Aegina for a day many, many years ago when I was on a group trip. It was a day cruise from Piraeus. I will venture to say that I think 3 nights on Hydra is too long. But as I said, my visit there was a long time ago.
Regarding visiting Aegina as a daytrip from Athens, it all depends on what you want to see in Athens. We spent 4 nights in Athens and skipped many museums and ancient ruins (for personal reasons I prefer not to go into) and we were not bored. We had a guided tour of the Acropolis, visited the Acropolis Museum, and then spent a few days wandering through the Plaka, Athens Flea market, Athens Central market (meat market and fish market, very unique), Monastiraki neighborhood, a lovely park, and saw the changing of the guard. There are plenty of museums and ancient sites we didn't see so there is plenty to keep you busy in Athens. If it were me, I wouldn't give up one of my 3 full days in Athens to go to Aegina, but you might have other interests.
Is the Meteora day trip from Athens as well? If so, you have very little time in Athens.
By the way, have you made your reservations? Is anything changeable? What time of year?