1.) Aside from the usual Santorini, Mykonos, what are the other Greek islands you would suggest to a first time Greece visitor? I've heard Paros and Rhodes. I'm also considering Milos?
Me I wouldn't even suggest the usual Santorini and Mykonos, so this is a very personal call you see : ) There are around 200+ inhabited islands in Greece and everyone could offer their own favorites and you would be no wiser. A couple of points to help you narrow it down is a) Travel logistics -see 4) below b) How busy you want it to be as for some islands it's very early in the season while for others it's fairly busy c) What you plan to do and see on each place, especially weather-related stuff, usually the southern/eastern you go the warmer the weather d) Budget issues, not only within the islands but also for getting there
2.) I want to make a side trip to another location I've been to Italy last year (Milan, Rome, Venice, Florence) so I'm thinking of Turkey, Cappadocia specifically. Is it a better option? Or I should visit Italy again and visit Positano side? Or do you have any other recommendations near Athens that's worth visiting and exploring?
As others said, you should do nothing. It's up to you. Do remember that Greece has a vast and varied mainland though and it's not only about Athens and the islands. Personally I would be tempted to explore a bit of that too, but that's me and not you.
Maybe not completely up to date, but to get you started to get an idea of ferry links, here is Greece-Turkey connections https://turkeytravelplanner.com/trans/Ship/GreekIslandFerries.html Greece-Italy ferries http://www.greekferries.gr/ There might be some seasonal flights between some of the Greek islands to major Italian towns and/or to Istanbul too, otherwise Athens is the obvious link for flights to international destinations.
https://www.aia.gr/traveler/flight-info/direct-flights/
3.) Also if I do push through with a side trip what's the best way to move? Via plane or train?
That really depends on specifics. In general the term "best" might mean different things to different people and/or under different curcumstances. A side trip where? Best on what terms? Money or conveniance or time-wise or what? Better to do some research and decide for your self after having some specific ideas.
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> 4.) While in Greece, flying to island to island. Is it better to ride a ferry or get plane tickets?
A major thing not to do while preparing a trip is to assume. It's common but wrong assumption among first time travelers to Greece when they start to plan a trip that everywhere is easily connected to everywhere. They can't be more wrong. Flights between the islands are not common while the ferry system needs some getting used to to see how it works. Very generally speaking, Greek islands are divided in island groups. Most ferry routes run within each island group and from/to Attica and ferries connecting different island groups are limited on specific routes and often only seasonal. It's more complicated than that, but a guidebook or playing around https://www.gtp.gr/RoutesForm.asp?lng=2 could give you a better idea on this. Please do note the time required to travel by sea, as an other wrong assumption is that "hey, A looks so close to B on the map, it mist be a half an hour deal", while in reality it might be a 7 hours ferry ride lol Do note that there are many ferry types too, the faster and smaller in general are more pricey than the larger and slower. Again a very general rule. It's not so terribly complicated as it sounds, but you need to get a handle of how these things work before making firm plans while been over-optimistic and haven't seen the practicalities...
5.) Or should I just ditch the side trip and enjoy the Greek Islands instead?
See replies above. Personal call.
6.) Any off the beaten track/non-touristy gems you'd recommend?
No, because they wouldn't be off the beaten track for too long lol On a more serious note, I feel you are at the very start of planning this trip. Browse this forum a bit and check a couple of guidebooks among other resources to get a better idea of the place(s), because to be honest your post feels mostly as name throwing. It takes some homework but a trip is always more rewarding after making some homework and customise a trip according to your own informed decisions, interests and specifics, rather than on other people's bias (including mine of course).
Do not hesitate to come back with more specific questions some time in the future and Do let us know how it goes
: )