What time of year will you be traveling? And have you looked at a map, and ferry schedules, and figured out the logistics of visiting the three widely-separated islands you mentioned? It's not exactly "you can't get there from here," but it's close.
As you may know, there are more than 200 populated Greek islands. They are divided into 7 groups. It is generally easy to travel within one island group. It becomes more complicated to travel between groups. You would be attempting to travel between three.
I know it's easy to see a beautiful picture or read an article and get fixated on an island. But I suggest that instead, you select one island group and focus on three islands within that group. Check any Greek guidebook. The Thomas Cook Greek Island Hopping Guide is especially good for a first-time Greek visitor. It doesn't have to be new ... you aren't looking for exact ferry schedules, just the general connections between islands.
Evia is its own "group", but along with the nearby Sporades islands, you could plan a lovely vacation with minimal travel complications.
I've not been to Hydra, as it seems to me to be a "Greek Island Experience" for travelers who can't spend an extended time on an island. And I would caution you on Kythira. I know it's beautiful; but I looked into visiting there once, and found that ferries to and from are sparse, which always creates the possibility of being stranded there for a day or two in case of a storm or ferry cancellation.