One thing to be aware of if you rent a car is one-way drop-off fees. These can be a few hundred Euro if you are dropping the car in a different country.
As for destinations, you are probably right to avoid London on Christmas Day itself as the shutdown is pretty much total.
Which places to visit really depends on what you want out of the trip.
If you are looking for lively cities, then Paris and Amsterdam are probably the answer.
If you want to experience a magical European Christmas, then Germany and Austria are impossible to beat. Christmas around here is simply another world, with Christmas markets, music, mulled wine and delicious food literally everywhere. (Ok, I'm a little bit biased!)
If you want the cities option, I would suggest a circle route with a few days in each place, i.e. Luxembourg - Paris - Amsterdam - Luxembourg.
If you want the Christmas magic, I would suggest making ypur was South and East from Luxembourg, through Alsace or the Rhine valley. Then through the Black Forest and across Bavaria to Munich and Salzburg and/or Innsbruck.
If you are flying KLM, it will be easy to get an open-jaw out of Salzburg or Munich.
By the way, Salzburg and Innsbruck are at least as nice as Vienna and not so far out of your way.