I've been to Rome a couple of times. It's wonderful. I haven't been in Winter though. I've not been to Stockholm. I get sick in northern winters, so not sure I will ever have a white Xmas.

Anyway. Rome is great with so much to do. Like Dantri, I adore Florence. It's one of my favourite places in the world. Venice is great to but I wouldn't go in Winter. You end up dealing with aqua alta which makes everything smell.

Otherwise, maybe a small town in Umbria or Tuscany?

Just note it is high season for flights, but many places close in Winter. Sights may not be open or they will have restricted hours, especially the Basilica at Xmas time. I'd research if places will be open for meals Christmas day. The Italians are extremely family oriented, so many things close for traditional family times (like Sunday). Rome is an international city though, so you'll find something.

Also include the cost of very warm clothes & research baggage restrictions.