Hi Babybab -
You have picked a good time to travel.
September is my favorite month - best chances for good weather (but, no promises. ;-) )
<<"Far from it, we love to experience the Alps, not just the cities.">>
You may find this interesting, and it might give you some ideas about the area around the Jungfrau:
Kim is quite thorough and very knowledgeable. You could spend many days exploring the region.
<<"We are also very much interested in visiting museums, churches, cathedrals, the chocolate train etc. We need to know how to go to Jungfraujoch.">>
You will find some nice churches and cathedrals, although I don't recall cathedrals on the scale of Yorkminster. ;-).
One of the nicest cathedrals to visit is in St. Gall:
The Jesuit Church in Luzern has a wonderful setting by the river, and has an impressive interior. 5 minutes from the main station. See attached image. I was lucky to have a fairly clear view of Pilatus in 2005 when I took that ; at dawn it is often hazy.
Also in Luzern are the Rosengart Collection, specializing in Klee's and Picasso's works, mostly:
which is 3 minutes walk from the main station,
and a small Picasso museum that we liked, in the old city about 5-10 minutes from the main station:
www.galenfrysinger.com /switzerland_luzern_pi casso_museum.htm
There are too many to name individually, but special ones include the Beyeler in Base, the Rietberg in Zürich, and Römerholz in Winterthur:
A powerful collection. ( A note- the small restaurant in this museum has nice, but short menu, with good food. They seem to take a long time to prepare even the simplest items on the menu, so don't plan on "fast food" here. ;-)