Hi Ankit -
<<"Day 4 Mt Pilatus or Mt Rigi. Spend time in Lucerne in the evening
Day 5 Go to Interlaken or Lauterbrunnen in the morning. Visit Jungfrau or Schilthorn
Day 6 Visit Bern during the day and come back to Interlaken in the evening (late)
Day 7 Interlaken to Geneva">>
Annika has already commented on Day 4. If you follow her links, you'll note that there are several routes to the Rigi. The one via Vitznau has the advantage of a nice lake boat ride. Also, I like that cograil ride up to Rigi Kulm for some great views over the lake. In my own opinion, the route between Rigi Kulm and Arth Goldau is less scenic, and has more sections without long distance views. The routes are close to each other at the top.
If you study the time table you can enter the trip from Luzernn to Rigi Kulm, then choose different options in the "via" or "connections" box. That will force it to offer different routes. I use the timetable a lot for trip planning, and combine it with a map:
map.search.ch/?x=17576m&y=20656m&z=32 &poi=bergbahn,halteste lle,zug
In that link i have turned on some "traffic" options under "Points of Interest " on the menu.
Day 5.- It is often recommended to take a t least a couple of days near the Jungfrau, as you have done, because the weather changes rapidly in the Alps, and you have a better chance of good weather for the trip up top. September is my favorite month for good weather, but, there can be very cloudy days. It is usually recommended to go up to Jungfraujoch in the AM, as clouds tend to gather during the PM.
Watch the weather reports, ask at your hotel or the local train stations, and chose between Bern and the Jungfrau ( days 5 and 6).
A trip to Bern does not have to take a whole day to be enjoyable. For me, the critical highlights take a few hours or half a day including lunch near the Nydegg Bridge or at the Rosegarden. More time could be needed, of course, if you look at museums, etc. If you stay in Lauterbrunnen, Wengen or Grindelwald ( or even Mürren, which takes a bit more time) you have a longer journey out to Bern, but it is not so critical to have good timing for that journey. If you stay at Interlaken (Ost) , you are only an hour or less from Bern.
If you stay at Wengen ( my own favorite) you are substantially closer to the Jungfrau, but about 50 minutes further from Bern. Lautebrunnen cuts about 30 minutes of that. The advantage over Interlaken is that is that Interlaken is not so much a tourist destination as it is a connection point for access to the rest of Switzerland. In contrast, Wengen and the other towns offer stunning scenery and the "feel" of being in the mountains. And, they give quick response to Kleine Scheidegg and up to the Jungfrau.
This small report may be useful:
Männlichen is particularly easy to reach from Wengen or Grindelwald. Pictures attached.
The Hotel Eiger is now an apartment building, but is very close to the station in Wengen.