Six days in Switzerland in June with my adult son with a six day STP

So, is this your first trip to Switzerland?
I see that last year you were thinking of basing in Bern, and are not up to hiking.
Are you a good walker?

Do you WANT to go up on one mountain?

If this is your first visit, I would suggest the following:
1) Get a Zurichcard at the TI in the main train station. Choose 24 or 72 hours.
This gives you a discount on the daily 90 minute public guided tour of Zurich + a few other amenities, such as a 90 minute roundtrip boat tour on Lake Zurich.

2) Visit Luzern, consider going up to Pilatus mountain by train. There is a complex at the top with restaurant(s).
Research Golden Roundtrip and Silver Roundtrip for two options to approach it.
The TI in Luzern can advise and sell tickets.
They also have a webcam to see if weather conditions at the top make it advisable.
The town itself is lovely, but heavily inundated with tourists, which can be a drag. Walk the town walls, climb the 3 towers if able.

3) Do visit Bern. I stayed for 2 weeks in an apartment a few years ago, and LOVED meandering the arcaded alleyways in the evening. This is particularly a good option for rainy days.
Have a beer in the old tram depot, look at the poor neurotic bears (city symbol) along the Aare river. Walk up to the Rose Gardens (if able) for spectacular views of the U-bend in the Aare river.
Note the numerous hundreds of years old city fountains. Eat potato Roesti!

4) IF you can walk well, there are many "hikes" above the Interlaken area along level gravel paths (research Grandmother's and Grandfather's walks).
These are stupendous whitecapped "peaks in your face" moments, accessible by gondola or other lifts.
5) Take a cruise on either Lake Brienz (the town of Brienz also has an "outdoor museum" =Ballenberg -accessible by bus, above town) or Lake Thun for yet another beautiful perspective!
Enjoy!

Thank you. It is my first trip and I want to make use of the six day STP that I bought.

Any reason why you picked 4 nights in Zurich and 2 nights in Thun? Not very good bases for visiting the Alps. Luzern and Lauterbrunnen would be better and reverse the days, 2 in Luzern and 4 in Lauterbrunnen, or at least 3 and 3.