Partly depends on your definition of mild...except for the Canary Islands you will likely still find quite cool temperatures requiring a jacket for most of the day. Also, don't forget that days are rather short and, as flyingfkb said it can get rainy and lots of the tourist infrastructure shuts down for the winter.
On the other hand, cities are a lot emptier and you can avoid the crowds.
We have been to Lisbon in early January and enjoyed it despite some rain, to Rome in late December (still fairly crowded but no comparison to summer) and to Venice in early February (empty, no lines, absolutely magic). On both Italy trips we got really lucky with the weather: sun and nice temperatures (around 15C).

I would choose a place where there is a plenty options inside and outdoors, so you have options if the weather is rainy.

Another potential area could be southern Spain (Andalusia) with Sevilla, Cordoba and such...