Greek Island in mid-December?

Boat timetable: www.gtp.gr. Don't go to small islands where everything is closed. Crete could be a good solution. It is not "close to the mainland", but there are many reliable ferries between Piraeus and the different towns of Crete. and there are a lot of hiking trails reachable by bus or taxi, minoan palaces, avery good archeological museum .....
Naxos is good for walking too, but you can't do there anyting else in December.

I am now thinking Hydra might be a good place to spend a week.

The absence of cars is very appealing!

If you like quiet Hydra is good but a bit of monotony in the winter. To my oppinion Crete is the best destination even in the winter (or probably winter is the best time to visit Crete) .

I agree that Crete would be a good choice however your first instincts are not too far off, If you have time for two locations, Naxos has a permanent population so it will have tavernas and hotels still open. I understand that the Olive harvest comes in in December and Naxos is covered with Olive groves. You may have a wonderful opportunity to experience typical Greek life as it has been for thousands of years.

My first suggestion is Hydra. It is a picturesque compact island, with magnificent stone mansions and a mild climate in winter [possibly due to the dominance of stone] It's permanent population totals approx 3,000, and it is very lively even in the winter months, as it is popular not only with the Athenians on the weekends, but also the day trippers from the one day cruise [2-4 pm daily] ..although this can prove rather annoying for some..

fly to crete (khania)... it won't disappoint

Try Spetses which is next to Hydra. 2 hrs on the flying dolphin from Pireaus port at several times of day, it is more spread out and great for bikes, walking in the hills or sea front, boat building is popular there and there are a few things still open even though it is winter. Hydra is monotonous at any time, there is mainly the port and lots of climbing of stairs. Spetses does not have cars like in most places, mainly bikes and some working trucks. I live in Spetses and I love the winter months. where ever you end up I am sure you will like it. We came to Greece in Winter in 1966 and went to 14 islands and you had to stay at least 3 days in each place because of the boat schedules then. Now you can go anywhere at any time. From Spetses you can also go for the day to Hydra and come back in the afternoon so that you can see it. It is a difficult place to stay for awhile, but it is well worth it to visit it and see it. Very beautiful and unique. have fun.

We've been to Naxos with my wife last February. I can only recommend it. The Naxos town is quiet but not deserted in winter, with quite lively waterfront, several restaurants and tavernas open, some shops and even supermarkets. The old town was a great place to get lost in the almost empty narrow back streets. There are several accomodation options open in the low season - we stayed in Pension Sofi which had nice rooms (with heating which we finally didn't need) and was reasonably close to the old town.

There are bus connections to the villages in the interior (departures at 7.30, 9.30 and 11 am) with lots of places for great hikes - depending on what you like there are mountains up to 1000 m, lower hills with small Byzantine churches and castle ruins, villages with fortress towers. Some village tavernas were open. Even if we missed the last bus back, the friendly locals always gave us a hike. Get a good topographic map (we used the Anavasi one) for it could be quite difficult to get through the olive groves on stony terraces if you lose the path.

The only drawback for walking was the fact that February was the bird hunting season (don't know how about December). There are not a lot of hunters (in fact we've met only one friendly guy in 6 days) but there were lots of empty cartridges on the paths. We just kept talking and singing loudly each time we were walking in covered places like olive groves. The hunter we had met told us that hunting was prohibited in the highest parts of the mountains.