Which Islands?

How much time do you have in total?
Are you looking to stick to public transport, or are you open to car rental?

Probably will stick to public transportation.

We also really need to know how long you have in total to suggest an itinerary. How long do you intend to spend in Athens? Have you identified other parts of the mainland you wish to visit? I highly recommend the Bradt Guide--I found it invaluable.
For a history lover, I can't recommend the Peloponnese high enough. I am a nature/sea lover too, and the area had all that as well, and I did not have to contend with crowds or ferry schedules. That's why I asked about the transport--I found it much easier with a car (and the driving was pleasant and easy), but many do visit the region without a car, it just requires more work to plan. Nafplio is a great base, allowing you to visit Epidaurus and Mycenae. Corinth/Arcocorinth, and Nemea are all on the way from Athens. Other places I would include are Mystras and Messene.

How many days do you have? (not counting the days of arrival and return) .

Regarding art and culture you will need to stay several days in Athens, and it all depends on which art and which culture. The Parian marble sculptures of the Acropolis Museum, the street art of the Exarchia district or the giant spider of Louise Bourgeois, it's art.

Maybe for some people going to crowd hundreds of people in Oia to photograph a sunset with their smartphone is art too..... who knows?

This is a very good info source for travel in Greece, including a section on the islands. We spent several days in Crete and liked it a lot, but it would be more suitable for a longer trip. We thought Hydra was less interesting than RS' recommendation suggests, but Hydra or Aegina might be a good choice if you only have a day or so outside the mainland. So your choices will have a lot to do with how long you have for this trip.

Santorini and Mykonos are very popular. I've been to neither, and have little interest because they're so crowded.

Thanks! We are pretty fluid with the time we will be traveling. I appreciate all of the help.