<<"Then later I thought this is my opportunity to ride up to a mountain peak! I ">>
Ooop! Sorry I missed your stated date earlier. I'll have to give up multitasking - eating a meal and typing at the same time. By the end of September, the higher elevations (up above 2000 meters or so ) might possibly have snow that would prevent walking on some of the trails if the weather hits a cold spell. October is when you really start to think about it, though. On the 12th of September, you can hope for weather like that in the attached images taken above Wengen near Männlichen on the 22nd of September in 2009.
You've got two tall peaks with great views in the Jungfrau region -
Jungfrau at 4160 meters +/- and Schilthorn at 2970 meters. Near by accessed from Wilderswil is Schynige Platte at about 2100 meters, and Harder Kulm(from Unterseen) overlooking Interlaken at 1300 meters
The weather often comes in layers....there might be a cloud deck at 3100 meters, with bright sunshine at 4100, etc.
The tourist offices and ticket offices usually have some kind of indication, including possibly a web cam, of what the weather is up on top. You'll have your pick of altitudes to be "at the peak." Choose your mountain!
The richness of scenery, trails, lifts, over a large area near the Jungfrau is unequaled among the choices you have mentioned.
That is my reason for thinking that Arno's recommendation is the way to go.
I suspect you know that the towns near the Jungfrau are mostly be car-free. You can take a car to Grindelwald (limited parking) and to Lauterbrunnen - large cheap parking garage. From those points onward, it is cograils and gondola lifts if you wish to go up. Sometimes, even chair lifts.
Lauterbrunnen also gives you access to the valley floor, if weather keeps you down. The waterfalls are worth a look. Attached image was taken from Wengen, and shows a bit of the valley floor south of Lauterbrunnen.