Don't stay in Geneva, nor in Zürich. Geneva is as far as you can get from the centre of Switzerland as possible, while still within the country. You'll add a lot of time to travel everywhere.

My suggestion would be to pick two nice places, for example on place in the Bernese Oberland (Wengen for example, but here I am biased as I live there part of the time), and another on on Lake Geneva. Vevey for example.
Switzerland is easy to get around in. The public transport system is fully integrated, basically like you would expect in a big city. It's a nationwide mass transit system.
Be aware that the weather is unpredictable. No travel plan survives contact with the Swiss weather. That is one reason to spend more time in the same place, so you can plan around the weather.

Get yourself a Swiss Half Fare Card when you arrive at the airport, and then just buy tickets from the ticket vending machines like everyone else does. Or get the SBB app, which is great both for planning and ticket purchases.
Then from the airport just travel to whichever place you've choosen for stopver #1, and start our adventure :-)