Thanks everybody for the feedback. I have been to some beach side towns that are almost all shuttered. Sounds like not only is not the case, but is a better time to visit if you want a less touristy experience.
I am not a Michelin star kind of diner, so no big deal there. Prefer mom & pop or off the beaten path kind of places. And we will have limited time, so the odd museum closing is no big deal. I like spending time strolling and as one poster above notes, lazy mornings with coffee and croissants.
The suggestion of St-Paul de Vence is great. That is the kind of place I would like to explore.
Thanks again everybody. Off to the Côte d'Azur in January it is.