The problem IMO is not that you have a car in Lucerne, the problem is the expensive, and maybe inconvenient parking. There are numerous parking structures around the city, so finding a place for the car is not that difficult. Will it be next door (or in close proximity) to your hotel? Maybe not. Lucerne is a great city for walking and exploring. I would not count it out as a base for exploration. DH and I will be there next weekend, with a car. One of my favorite cities!

Kandersteg may not be the best place for what you are intending to do because:
There is no road from Italy to Kandersteg. Coming by car from Italy, you will have to cross the Simplon Pass (2000m/6600ft), go down to Gampel (600m/1950ft) and by local road to Goppenstein (1220m/400ft), where you can board a car shuttle train which brings you to Kandersteg.

The only road which connects Kandersteg with other parts of Switzerland is not very fast (steep gradients, many curves). Therefore, car rides from Kandersteg to Monteux or Lucerne will last longer than 2 hrs one way.

I could give you a long list of alternative places, but for that, it might be useful to know
from where in Italy you will come (Montreux for example is just between Turin and Berne),
to which place you want to go after Switzerland,
if you really want to stay all the time at the same place (may be it would be easier to sleep every night at another place instead of backtracking all the time),
if you prefer to sleep in a rather small mountain village (like Kandersteg) or in a town with a medieval centre, museums, night life, etc (like Lucerne9.

thank you very much for your replies. we will be driving from Bellagio to Switzerland. After that the plan is to go from Switzerland to Annecy and then to Lyon where we will be dropping the car off.
I would love to stay in Lucerne, and then move elsewhere for the remaining days.

simpsonc510- yes you are right about the expensive and inconvenient parking. Perhaps you could suggest somewhere to stay in Lucerne.

Kanderstag is too isolated.