Greece in Spring?

I found May fantastic weather-wise, plus crowds were low on the Peloponnese (we spent minimal time in Athens, none on islands). We were able to swim a little in late May, but only as part of long hikes. Water in the Med (for your Croatia consideration, where my advice would be much the same) takes till June to warm up. If swimming is a priority, I would go in September or early June.
I have visited Croatia several times, and that is partially why I skipped the Greek islands. I also only had ten days and I wanted to spend them not going on and off ferries. That part is a lot of legwork, so I would focus on that part first and suss out a good website with comprehensive ferry info. You may want to focus on one island group where the ferries are more efficient. At the minimal end of research, you can zoom in on Google Maps and see the dotted lines that indicate ferry lines (I find that helpful anyway). Good luck!
You can check flights to islands as well, several have airports.

We did the RS Best of Greece tour in late March early April before Covid. I thought it was a great time to be there because the wild flowers were beautiful, the weather was mostly pleasant temperatures and it wasn’t crowded. We did have one day of rain. Not a time to go if you want beaches, the water was still cold. The island of Hydra was absolutely beautiful with the fields full of yellow flowers.

Is Spring a good time?

Spring is the best season to go to the Greek islands. Prices are lower, there are fewer people and the weather is perfect. However, until late May you may find the sea too cold. That's about the only drawback.
I usually go between mid-May and mid-June. Otherwise I wait until at least mid-September when the crowds have left.

Appreciate any ideas for choosing islands, how long to spend where,
etc.

Island hopping in the Greek islands is almost a science in itself that requires a bit of work in advance because the ferry routes are not specifically designed for tourists. Don't imagine that you will be able to go from any island to any other via a direct ferry, even in the same group of islands like the Cyclades, and even if these islands are close to each other.
Just the trip from one island to another often takes a good part of a day. It is almost like a lost holiday day.

Many ferry companies do not publish their schedules very far in advance, sometimes only 2 months.

Use ferryhopper.com to check them

Whatever the island you need to plan at least 3 full days (4 nights) to enjoy it, hang out in villages, visit vineyards or local producers, go hiking, discover hidden beaches, etc. (my average is 5 or 6 nights and I always feel that it is too short). A car is usually essential if you want to explore the island without being dependent on buses that rarely go where you need when you need.

The islands have an official website, use it preferably and avoid social media influencers

Is there an alternative to flying in and out of Athens?

From many European cities there are, roughly from May to October, quite a few direct flights to Santorini since it is a mass tourism destination. This can be an option and Santorini can be another starting point for island hopping in the Cyclades. The disadvantage is that it requires you to stay at least one night in Santorini to take a ferry the day after your arrival flight. Even if it may seem strange to say that it is a disadvantage to go to Santorini, there are many Europeans who want to do island hopping but have no desire to stay in Santorini.

My one trip to the islands was in mid-October, when tourism was winding down. I flew into Heraklion (there are some international flights) and spent 5 nights in Chania (loved it), then 2N in Heraklion for a full day at the archaeology museum and Knossos, then took the ferry to Santorini for several nights. Even though it was the end of the season in other places, Santorini was still very crowded, with 1 or 2 huge cruise ships in port every day. From there I took the ferry to Naxos for several delightful days and the best beaches, then flew to Athens for a return visit. Athens is well worth 2-3 days, at least.

You need to get to the ferry in Heraklion about an hour before departure. Then it takes about an hour to disembark in Santorini, find your reserved transportation and drive into town. Getting back to the port takes somewhat less time and you don't need much lead time. In Naxos, my room was a 10-minute level walk from the ferry.

Thank you for the responses so far. Are there ferry routes that run consistently for rough planning? Or will I need to wait for published schedules and plan from there?

Brad

Are there ferry routes that run consistently for rough planning?

In spring it is totally useless to book in advance (except for a few exceptions during Easter week) and worrying about whether there will be seats available should not be a concern.
The important thing is to know if there is a ferry connection between two islands or not, and if so how often (daily, 2 or 3 times a week, etc.).
A few weeks before the trip, it is easy to check with for example the ferryhopper website.

https://www.ferryhopper.com/en/#/

Several months in advance you can refer to the schedules of the previous year that you can check on openseas.gr

http://www.openseas.gr/

There is no guarantee to have the same itineraries and schedules from one year to the next but if you are not used to traveling between the islands it is a good indicator, at least to know if you will find a daily ferry or a ferry only 2 times a week.

You can also have preferences about the type of ferry, highspeed catamaran or conventional ferry. There is a difference in price, speed, comfort, atmosphere. The same trip on a Seajets highspeed catamaran can be a little faster than with a conventional ferry but can cost up to 4 times more.

It is also good to keep in mind that there may be delays or cancellations of ferries due to bad weather, technical incidents or even strikes.
So if you want to visit Athens keep these days at the end of your stay. Being stuck on an island for a day or two is an unforeseen event that can happen and you don't want it to happen while your flight home is taking off.

Note that you will find beautiful beaches, white washed houses and blue domes in all the Cyclades islands. Do not let yourself be manipulated by tourist marketing, social networks and other Instagram photos that promote 4 or 5 islands out of the 20 Cyclades islands.

Islands like Sifnos, Andros, Kythnos, Tinos, Amorgos, Kimolos are real paradises that have not yet been spoiled by mass tourism.