I enjoyed a 3-day stay in Aegina, it's very handy for people who want a close-by island to combine with AThens... but I am puzzled by a decision to stay there for 3 Weeks. Have you already visited 15-20 other islands, and just want a nearby place? Where are you from? What time of year trip? (in high season, it can be packed with Athenians).
AHA. I just clicked on your name, and found your other posting in which you gave more details ... TIp for Future -- even tho you say "as posted before" please do repeat key facts. Now I know --- you're British retirees, looking far ahead, to May 2020 (great time of year BTW), and apparently you like to unpack once, & stay put. Hmmm. I have UK friends like this, who use Greece somewhat as N. Americans use Florida ... a getaway to nicer weather, stay in one place, some day excursions... not particularly intent on ancient sites or famous landmarks that "New World" people come looking for. Can always come back next year, at moderate cost, a compared to "once in lifetime" trips for many USA tourists.
We're all envious of your 3-week stay, and (as u know) May has many plusses; rain is gone, but greeenery abounds, temperatures mild, everything's open/nothing is crowded, the Greeks are refreshed, happy about weather, busy with summer prep, but plenty of time to socialise. Good choice! However I agree with others that it's island-Hopping.. not Island-Basing. Why? A few reasons -
• Day trips can mean at least half the day on ferries, with perhaps 4-5 hours max on an island ... which means you'd be limited to walking the harbor, maybe taking a quick bus trip
• Most feasible trips from Pireaus are on costly "fast ferries" --once 2x cost of slower conventional open-deck ferries but now I hear are waaay more €€€now. So the round-trip ferry for 2 would cost a lot more than a night in modest lodgings.
• Fast-ferries don't have open-decks, you're pent inside, no walk-around room, limited views.... hours of boredom!
Have you considered perhaps FOUR easy-too-reach islands, where u could spend 5 days on each, going from 1 to next in ferry trips of just 1-2 hours instead of lengthy backtracking? I have had wonderful experiences this way... and on a shoestring budget. Since you're prudently planning so far ahead, I could recommend wonderful very moderate small hotels/guesthouses I've loved in May & early June, in wonderful islands like Sifnos, Serifos, Naxos, Paros, Antiparos, Folegandros, Milos ... and this is just the Cyclades group. Each of them has a port or village(s) fascinating to stroll & explore.. many have good bus networks foro further exploring. If you haven't a guide book, this link https://www.greektravel.com/greekislands/ can give you a great overview... and if you want more, a click on each island will give you a dedicated illustrated webpage on each. We look forward to you coming back with some preferences, and we can get started helping you witih this dream trip!
PS: It sounds as if you mean to start by going to France ... if you want travel and hotel advice for that, you'd do better as others hve suggested ... and a train journey to Greece is not feasible, barely possible. IF u must start with Paris, then fly from there to Athens and take a bus immediately to Pireaus.