2 weeks trip starting in Paris then down to Strasbourg then around Basel. December 23rd-27th then into northern Italy.
What's it like in Basel or Lucerne around xmas time? I'm reading about closures on 25th/26th which we can work around.
Should we look into larger cities for that time or...?
Yes, stores will close early on the 24th, usually 5:00pm and since the 27th is a Sunday that means they will be closed Friday 25th - Sunday 27th and open again on Monday.
Exceptions, can be shops located in the larger train stations, small gas station shops, Coop Pronto (a small version of the Coop grocery store), things like that.
Public transportation runs as usual and most restaurants will be open as well - some needing reservations as this is a busy time for families and groups to eat out together.
You can take a look at the websites for Basel and Luzern to see what things are planned over Christmas such as the dates of markets, etc. To get an overview of many locations at once you can look at Switzerland tourism
https://www.myswitzerland.com/en-ch/experiences/winter/christmas/