If you go to Morocco, don’t expect it to be warm. Our visit there was in mid January 2019, and while it wasn’t sub-zero, it was cool enough to need a jacket both day and night, with additional layers when it was unquestionably chilly. This was both in and around Marrakech, Fes, and in the desert beyond Ourzazate.
In 2012, as part of a longer Italy trip, we’d begun the last week of the year in Sicily, then ferried over to the mainland to work our way north to Sorrento. We had a car, and did mostly one-night-stand stays that week. We actually then stayed for several nights in Piano di Sorrento, and it was neat seeing peoples’ individual fireworks displays all over town at midnight on New Year’s. Later that morning, Pompeii was supposed to have been closed, but it was open until 1pm, and not crowded, except for one large and very loud tour group. Southern Italy, whatever city you picked, wouldn’t be too hot, nor overwhelmed with crowds.
Or, what if you embraced the cold, and went to Iceland? Again, no swarms of tourists. Any ski destination in Europe might be fun, but would be the most expensive week of the year.