Hi Kauriejnee -
You did not say how long you will be in Switzerland.
Do you have any special interests besides train rides? Hiking, museums, lake boat rides.....?
I like to visit Switzerland in late May or early June myself. However, when I do that, I don't go up into the Alps that are mentioned by Lucas. I tend to visit the cities and countryside at lower altitudes.... and I do like to walk in the countryside.
Altitude is everything,
and, in general -
and, although there are some nice train rides and cableway rides ( to the villages mentioned or the Jungfrau or Schilthorn), the high trails above 1500 or 2000 meters are generally snowed in until mid-to late June ( depends on snowpack). It's too early for hiking on high but the snow is no good for most skiing, so there are few customers. The floor of the Lauterbrunnen Valley (at about 700 meters altitude ) will be nice. The villages tend to be very quiet, and many,but not all hotels and restaurants don't really open up until mid-June. Some will be open.
Check the links under that main heading.
The Swiss rail network, as you have apparently figured out, is really good for the base+day trip kind of travel that you plan.
Please make sure that you study the timetable thoroughly. There is a tremendous amountof information buried in layers and menus. The introductory page here is valuable:
Also, the main SBB website has a lot of useful data:
You can find out about various services with different speeds and costs to transfer luggage from station to station ( I use it often) :
and also details of the equipment, services, and opening hours for various services at each station:
Under "Stations and Services" on the home page enter the name of a station in the box labeled "Find your station.".
Here is what I get if I follow the menus for Luzern:
Look under "Services" and "Equipment."
Famous towns with excellent rail connections in many directions include Zürich, Luzern, Bern.
As you get further awy fromm big city hubs, the frequency of service diminishes, but there is almopst always service once per hour from early morning until the veening...and late at night on the main lines.
Zürich is an interesting town, but is not in the Alps and is not usually the best city for sightseeing. On the other hand,the density of cultural features is high....museums, etc.
We usually put Luzern first on the list of base towns, but others can make sense, too.
and - in general -