First time to Greece. Islands or mainland, or both?

It all depends, which islands and which part of the mainland? You could definitely include an island or two and perhaps a couple places on the mainland in a two-week trip, but it's all in the details.
This was an easy decision for me because of my interest in nature and archaeology, and because I wanted to have a simple driving trip and not deal with ferries and moving around a lot on my ten-day trip. (I went to the Peloponnese.) I would get a Greece book and start flagging which places sound the most appealing to you, noting transport logistics, and then see what ends up getting the most flags. The only mistake you can make is tying to cram a month's worth of stuff into a two-eek trip, and that will all get worked out in the planning if you post your tentative itinerary here, so first focus on what kind of trip you want. Good luck!
I will plug the mainland as being gloriously uncrowded (late May anyway) and full of treasures, with just as much nature as any island would offer. I will definitely be coming back to see more of the mainland and eventually get to some islands too, so always plan to make the best of your time but with the plan to come back!

I think two weeks would be enough time to visit at least one island as well as mainland places like Athens, Nafplio, and Delphi. Naxos has a good reputation on this forum though I haven't been there. Aegina (also well regarded here though I haven't been) is easy to reach as a day trip from Athens. But I agree that "fewer is better" instead of trying to pile up too many places in limited time.

Matt Barrett's website has a wealth of information about what to do in Greece and how to do it.

THe vital fact, which you have not included, is WHEN. It makes all the difference -- timing affects everything! Opening hours, heat, costs, crowds, availability of flights, ferry schedules, local busses etc etc, sports options. Late May/early June or Sept = optimal times. Experience is VERY different in Winter/early Spring or HIGH Season of July/August. You can't get useful advice without supplying useful info. Share.

Give yourself 3-4 nights in Athens and 3 in Santorini and you're good to go. Fly to the island instead of wasting all day on the ferry.

SCroll to my post, I did two weeks in both and had a blast.

Thanks to all. We're trying to figure out where to go January/February/March and Greece seemed like it might be a possibility. Don't mind the colder weather, just want access to museums indoor and outdoor, lodging, and restaurants. Prefer to avoid crowds at this point because we don't know where the pandemic will transition to next.

Jan/Feb/March will not be beach weather. The water will be chilly at best so kayaking & sailing may not be enjoyable unless you are bring wet suits.

Lots of museums just about anywhere.

You may want to check on weather conditions for those months on where to go.

If you want an island I would suggest Crete as it's the southern most of the islands where you'll have a better chance of decent weather.

Crete is the largest of the Greek Islands and you could spend your entire 2 weeks there and still not see it all.

Crete is filled with history going back to Minoan times and continues right up to now. Wonderful museums throughout the island.

Lots of options all over the island in all parts of Crete.

I would combine Crete and Athens. Athens deserves a minimum of two days with three better.

There have been some questions here about traveling in winter, I would definitely seek out those posts for info on the best islands for winter travel. Crete and Rhodes are the ones most often mentioned as being more suitable for winter visits if memory serves. But there is plenty to occupy you on the mainland at any time of year.

Crete is a good idea for those months. If you prefer smaller islands, choose something as far south as possible; it does make a difference in terms of weather and temperatures.

The weather can be quite unpredictable in those months. You can have sun one day and pouring rain the next, thunderstorms or even snow. Make sure to plan for unexpected events like canceled flights. We've had that happen, everything coming to a stillstand because of 2 mm of snow. We sure were glad we had gone to Athens a day earlier than we had to!

With the exception of Crete maybe, those months are totally off-season which has advantages and disadvantages. We loved having the islands to ourselves... practically no tourists. Many locals go to Athens during the winter months, so on the smaller islands, a lot of restaurants etc. will be closed.

Don't expect accomodations to be equipped with efficient heating systems. You may only have the air conditioning system for heating, which it is not made for, and it may not get the room above 15° C.

I am not into water sports so I really can't speak to that. I will venture to recommend though that you take into account the unpredictable weather of those months. The Greek gods of the winds are something to keep in mind all year. :-)

Any thoughts about going in March?

In terms of what? It's still going to be cold, but possible better than Jan-Feb. You can check weather stats on a site like wunderground.
I would not plan on any water sports, but it will probably be nice for hiking.

Any thoughts about going in March?

Not sure who you were addressing with this question... As far as I am concerned: I was talking about March. :-)

Again, check weather conditions for where you want to go and what time of year.

March, especially late March will be better with early April even better.

Depends on what you want to do, forget the beach or swimming but lots of other activities like visiting out of the way villages, museums, walking, hiking, driving around back roads and always great food regardless of time of year.

Don't let the weather dictate what you want to do.

Always be prepared for whatever the weather throws at you and you'll be fine.

Thank you Tommy & Anna. We usually don't let travel dictate our travels, e.g., NYC, in January or February, etc. Iceland, pretty much any time is cold. So, I thank you for your advice. We like the idea of no crowds as it makes for a more authentic experience.

I've been to Greece twice. In late April to early May 4 years ago (RS tour) the weather was pleasantly warm and sunny, the water was icy cold. Folks who were brave went in but not for more than a few minutes and that was on pretty warm days. That year another RS forum woman took the tour in late March and said it tended to be rainy and chilly. To get a better idea, use this website to find daily weather conditions for a town for any month for the last 10 years. (To be helpful, the link takes you to Athens March 2021).

My second trip was in mid-October 2 years ago, mainly to Crete, Santorini and Naxos with a few days in Athens at the end. Santorini and Naxos were both shutting down for the winter. I had the impression that Santorini doesn't complete shut down, but Naxos was about 60-70% closed already. That means no rooms to rent, few cafes/restaurants open and for more limited hours, no tours and much curtailed ferry service. Chania and Heraklion will probably be fine in March, without crowds but most places open. Athens is definitely a good choice any time of year.

A lot of the Peloponnese would probably be opened up by March. It's not so easy to get around except by car.

Santorini and Naxos were both shutting down for the winter. I had the
impression that Santorini doesn't complete shut down, but Naxos was
about 60-70% closed already.

That is my observation exactly. The farther north you get, the more is shut down.

That means no rooms to rent

I beg to differ... from my own experience on some of the even smaller Cyclades islands. Our experience was that yes, it's totally impossible to book anything like a package vacation during those months, except on Crete and possibly on Santorini. We took the risk and went there without having booked rooms ahead of time. And while many hotels were in fact closed for the winter, it was no problem at all to find rooms. Au contraire! The locals who usually don't have an income from tourism during winter were only too happy to rent out their rooms for a couple of nights. We got a big studio apartment for a rate that was so low that made us almost feel ashamed. (Just remember being warned about the heating...)

few cafes/restaurants open

That is certainly true. Surprisingly, that wasn't all bad either. Since we were the only tourists far and wide, and they were one of the very few restaurants that was open, we went to their place several times, and it was fun getting to know the owners and getting to talk to these locals a lot more than during the busy season.

It's not so easy to get around except by car.

As far as the islands are concerned, I'll have to beg to differ here too. :-) The bus system on the islands wasn't primarily installed for the tourists' convenience. It's for the locals. The children have to go to school in winter, people have to get around. So the bus system may run on a different schedule than during tourist season, but it certainly is in effect.

I've been traveling to Greece every October for years, usually the first half (exception for last year/this year due to Covid)

Obviously that's not winter months or even March.

However, from my observations while the tourist season is closed that doesn't mean Greece shuts down.

They'll always be shops, markets and tavernas open for locals which in the end will give you a more "Greek" experience rather than a tourist experience.

Locals will be more relaxed without having to deal with tourists. Prices for accommodations are less expensive, far less traffic on the roads and weather will be dependent on what time of year you go.

I think off season is a great time for Greece depending on what you are looking for: touristy travel agent Greece or a more laid back and traditional Greece.

Here's another tip for you: If you decide to go during the winter months, it might be a good idea to find a room with a kitchenette. That will give you a bit of independence from restaurants being open or not. Grocery stores will be open for sure; the locals do have to eat too.

And it will give you some openness for serendipity: One day, walking through town, we saw a car with an open trunk, surrounded by people and all the hungry island cats. It was the local fisherman with his catch of the day. Of course we got some and made a great dinner for ourselves. It was probably the freshest fish we've ever had.

I went to Greece for 13 nights. I went to Nafpilo, two sites in the Peloponnese, Heraklion and Chania in Crete for 2 nights and 3 days, Delphi, and Athens. I would have been as happy if I had gone to Olympia in Western Greece and skipped Crete. There is more than enough to occupy you on the mainland for 2 weeks. There is enough on Crete to occupy you for 3 to 6 or more days. Read Rick Steves guide. The Rough Guide to Greece is good too. If you ever go to Crete, buy the Rough Guide to Crete. Skip Islands for your first time in Greece. If you go back to Greece you could see about Crete, Rhodes, and/or other Islands. I have no clue what is on most islands. I wanted to see museums and old ruins. I didn't care much for beaches and outdoor activities. I could travel in Michigan in the summer if I want beaches and outdoor activities.