First Time - Hydra or Milos for laid back solo island trip?

I haven't been to either, so I cannot comment on or compare them.
I thoroughly enjoyed Aegina, which is about a 40 minute ferry ride from Piraeus (the primary port for Athens).

Pleasant harbor town, nice hilly terrain, ancient temple ruins, easy-ish to get around (I rented a car while staying in Ag. Marina, as the cab cost was 17 euro each way between that town and Aegina Town. There's a bus that circulates around the island, but the schedule didn't seem to jibe with my needs for the time I was there).

Ag. Marina has a nice sandy beach. That's the only one I went to during my visit.
I wish I'd bought back more pistachios. They were different that what I am used to in the USA, but very flavorful. People on Aegina will tell you they grow the best pistachios anywhere.

I wouldn't want to stop you from going Hydra or Milos but maybe you could start by reading some travel guides about Greece. Or go to:

https://www.visitgreece.gr/islands/

You will see that there are a few other options (around 200) of islands to visit other than Hydra or Milos. Whether you have one or 2 weeks also changes a lot what it is possible to do / visit

Hydra or Milos are options but there are many other islands that offer more.

I would also recommend more research on Greek Islands as you'll find many others that may provide more of what you are looking for.

April will be off season so most islands will not have all their tourist infrastructure open if that's important.

Otherwise most islands will have enough services open for locals which will give you a more "Greek" experience rather than a tourist experience.

Check out this website for Greek Islands:

https://www.greektravel.com/greekislands/

Several years ago we spent time on Milos and Sifnos. We greatly preferred Sifnos which felt more authentic, had nice beaches, good food, and friendly people. Conversely, Milos was more touristy and less friendly. Loved Sifnos and hope to return. Would try another island rather than return to Milos.

Hydra seems most often to be recommended to those who want to see a Greek island but don't have enough time to get terribly far from Athens.

We greatly preferred Sifnos which felt more authentic, had nice beaches, good food, and friendly people. @mml

Thank you so much for the super helpful insight! I hadn't looked into Sifnos. This sounds like a much better fit! Really appreciate you sharing!

Hydra seems most often to be recommended to those who want to see a Greek island but don't have enough time to get terribly far from Athens. @acraven

This is great to know! I'm doing a lot of research trying to decipher what it super touristy or not. Your feedback makes sense! I have time to travel further so seems like I would enjoy another island more. Thanks!