It depends largely on the time of the year when you are travelling, if you are going in the next weeks, mountain areas are snow covered and access might be difficult, if we are talking May/June, the situation looks differently.

Despite Bern being in the center of Switzerland and being a good base for the Bernese Mountains, I would not base myself there for too long. It's a very nice city, indeed, but you have seen it in 1 day and it's basically government business. Geneva is not a very good place either to base yourself unless you also want to travel to neigbouring France. Again, the city itself can easily be seen in 1 day. I would rather base myself in Lausanne (closer to Chateau Chillon and other nice places and easy day trip to Geneva possible). Then I would consider Lucerne or Interlaken (possible day trip to Jungfraujoch or Schilthorn) as a base as these are more centric points for many tourist places than Bern or Zurich.

Zurich is good in terms of transportation as you get easily everywhere from there, many food and drink options, but again the city can be seen in 1 day like any other Swiss city. Think about visiting the Rhein Falls, Switzerland's biggest (not highest) water falls, if you have spare time in Zurich.