A few thoughts.
It will be winter weather - Greece is not warm in the winter months. Quite cold, possibly windy and rainy.
Have you investigated ferry times? If not, I would not assume that there is an afternoon ferry to Kea - not saying there isn't, but ferries in January are unlikely to go more than once a day, at whatever time it goes. Ferry schedules will be different in winter, so it may be hard to establish at this time what will be possible. The same thing applies for the ferry returning - you may not be able to get a morning ferry that leaves you enough time to drive up to Delphi. The roads are narrow and winding through the hills approaching Delphi, and I wouldn't fancy driving them in the dark.
Whether Kea or Hydra, be aware that in January it will be very quiet on the island, possibly with a lot of hotels closed for the season. You should be able to get great hotel deals everywhere you go. There's no need to make reservations until a day or two before you go. For sure, don't make unrefundable hotel reservations on the islands until you have ferry tickets in hand. It's not unusual for ferries to be cancelled. Santorini may be more awake for tourists than most of the islands, but you are still far off season, so it is likely to be pretty quiet. The views will still be there, however, and it's unlikely you'll encounter the cruise hordes that plague the island in the warmer months.
Just know that you are talking about a whole lot of driving Athens-Delphi-Kastraki-Athens. Most of it is challenging driving on two-lane roads. The first about half of the trip from Kastraki to Athens is on winding two lane roads and will involve a lot of tricky passing if you don't want to be stuck behind very slow traffic. Then it joins the major highway and the traffic will blow by you like you're standing still, which can be unnerving too.