What type of non-diving activities do you enjoy? Are you looking for land-based or liveaboard diving? How many days will you be traveling? Can you give us a relative idea about your budget, is it small, medium, large?
When you say "easy" do you mean "easy to get to", "easy diving", "easy (valet) dive operation" or something else?
When you say "few sharks" does that mean that you are looking for shark encounters or that you prefer low shark places?
The end of December and early January is a high travel season to warm locations so crowds may be an issue in lots of places and prices will be at their peak.
Sorry to ask so many questions, but it's a big world of diving and more information would better help us to advise you.
Based on your location, the Red Sea would be near and offers wonderful diving, but many people have concerns about traveling to the Middle East at this time.
@Storker recently reported a positive experience diving Tenerife in the Canary Islands which would be pretty close to you, but I think that the water will be quite cold at that time of year; but since you are used to the Mediterranean, maybe that isn't a concern?
Based on the information you provided, I am going to recommend Little Cayman. It has some of the best diving in the Caribbean, you are likely to see a few sharks, also lots of turtles, groupers, eels, and many tropical fish and beautiful reefs.
The reefs are close to shore and there usually isn't much current. The walls are amazing but they usually start rather shallow so it is easy diving. It is a small island and will not be crowded (but you'd better book soon because it fills up fast!)
There's not much night life, restaurants, shopping, or tourist attractions, but if you like those activities and you have the time, you could spend a few days on Grand Cayman.
Below is the link to the place we like to stay on LC, it is a small, all-inclusive, diver-dedicated resort with an excellent onsite dive operation that provides valet dive services. Everything is easy. And there are few other places to stay on Little Cayman if you prefer.
Little Cayman Beach Resort | Cayman Islands Resorts