Currently me and my wife are looking at 14 days from late Nov to early Dec with 5 days in Nice, 4 days in Venice, and then back to Paris for another 4 days before flying back to NY. We figure 5 days should be enough to see the Nice, Eze, Villefrance, and Monaco area but is it worth it to try to squeeze in some parts of Provence? I've never been to the south of France before and I'm not sure the time would be worth it since in winter you won't see the famed wildflowers and the waters will be too cold to swim in the Calanques. Does anyone with more experience know if there are any cities in Provence that are particularly charming in Winter or we should just save the area as a whole for another time?
It can be surprisingly cold in Provence during the winter, but I can't speak to what there is to see and do then. Provence warrants more time and I would say do it on another trip, preferably in late spring or early summer...the lavender peaks in July.
While occasionally cold, Provence is worth it in the winter, but you do not have time: it is 3 hours away from Nice, and I wouldn't go to that region for anything less than three days!
Best to enjoy the Nice region. You can add places such as Menton or St Paul de Vence to your list if you feel that you have extra time.
I suggest Googling "mistral". You might or might not get lucky.
Definitely research the opening days/times of any indoor sights you want to see, even along the Riviera. During my May 2017 trip I noticed that a lot of places close one extra day a week outside of peak summer season, and some close an extra two days a week (or, rarely, even three!) as you get into late fall and winter. If you know what they're doing ahead of time, you can plan to visit places on a good day of the week rather than just showing up and being disappointed.
If you get cooler-than-expected weather, keep in mind that Menton is supposed to be the warmest spot along the Riviera. It has an atmospheric medieval center which I'd hope wouldn't be overrun by tourists in late November. There are also two hillside gardens I enjoyed--but I don't know how worth visiting the latter would be off-season.
I agree you probably don't have the time, especially since it is you first stop. I would simply add more day trips to your Nice itinerary versus trying to squeeze in a trip to the countryside. Note that some businesses in the smaller Provence villages may actually shut down, or at least for November and/or January (some come alive in December for Christmas markets). This is even true in the Nice backcountry/mountains. The larger towns will be fine.
I am not at all a fan of Provence in the winter. There are periods where it is actually warmer in the north of France than the south although that is quite relative when you are not planning visits to the beach. But my main complaint is that too much of Provence is totally dead in the off season -- lots of restaurants closed, villages that seem abandoned, landscapes that can be dreary if the sun is not shining... My destinations of choice in the winter are actually all in the north -- Lille, Metz, Nancy, Strasbourg, Brussels, Luxembourg, to name a few. They know how to deal with winter and are very lively with all sorts of events to help keep them warm.
Actually, November 1 to April 1, a lot shuts down in the south.