If you just want T-shirt weather during the day and a generally, reliably mild climate all the time - I've loved Spain for many January breaks. For the best weather, look at the southeast, around Málaga, Granada, Ronda - for some reason that corner seems to get the most hours of sun and fewest of rain of all of mainland Europe in the winter. Maybe even north along the east coast to Alicante and Valencia. But I've also loved Sevilla, Cádiz, and Córdoba - still southish, but further west - in January too.
For Greece, I'd be careful of the islands only because many things may be closed. I'd look at Crete, maybe, or mainland Greece may be a better option. Or Cyprus?
Malta's also a nice warm-but-not-beachy temperature, but expect about 1/3 of your days to be rainy, and often accompanied by high winds!
I was in western Turkey a few years ago for the whole month of March, and it was a mix - some days hot all day, some soooo cold!
Caribbean's ideal for the temperature, a medium-length flight, and OKish for COVID (although I think things are declining in general in the region) but if you disliked other places you may not love Barbados - maybe we can advise better if you tell what you disliked?
As an outside choice (long flight), I loved Cambodia in late February/early March. There's a high season which is nice but hectic and expensive; if you get in on either side of it, it can be a very relaxing trip.