Here is a start, in addition to the links that Lucas provided.
What languages can you use? Besides American English, that is?
Here are a few museums that are well worth a visit.
Two of my favorites:
The only defect is that even the light meals in the small cafe take forever to be prepared and presented. ;-)
Really nit-picking, don't you think?
Winterthur is a short train ride from Zürich. the museum is a 10-15 minute walk from the main station in Winterthur.
This one is a real powerhouse:
3 minutes from Luzern main station
the Rietberg in Zürich has an exquisite collection:
That is just a start of course.
With the time you have available and the time of year you are traveling, a reasonable plan would be to fly into Zürich and transfer immediately to Luzern ( about 1-1.5 hours away by frequent trains).
Stay there a few days, appreciating the variety, and using it as a travel base, and include some nice hiking.
Then, and transfer to the Bernese Oberland, near the Jungfrau for 3 or 4 days. Best to allow several days in case the weather up top ( Jungfrau, Kleine Scheidegg, Männlichen, First) is cloudy... Changes rapidly, but not easily predictable.
The town if Schwyz, not far from Luzern, is interesting for its history.
This is a useful map. Play with the overlays under Points of Interst/Traffic (and Gastronomy- which includes hotels...)
Zoom in for train lines.
This will help you plan your travels:
If you are intersted in the culture and history of democracy in Switzerland, this link will be informative:
You also might enjoy Professor Steinbergs's book - "Why Switzerland, 3rd. edn., Cambridge Univ. Press.
This review of the 2nd edn. is relevant:dannyreviews.com/h/Swi tzerland.html
smile.amazon.com/Why-Switzerland-Jonathan-Steinberg/dp/052170955 5/ref=sr_1_1?ie=UTF8&qid=1483730348 &sr=8-1&keywords=why+switzer land+steinberg