<<"We are travelling from a far country, it is a rare opportunity for us to visit Switzerland, so that we want to visit many beautiful places in Switzerland.">>
I understand. Do your best to sleep on the plane. Luckily jet lag traveling from East to West tend to be a lot less potent than jet lag from traveling West to East.
<<"The reason we don't want to spend a lot of time in Geneva is because we prefer to see panoramic view instead of city/buildings. Unfortunately, few months ago I made a mistake in planning, I already booked and issued flight from Geneva to Rome so I have to stay one night in Geneva before fly to Rome, so Geneva is my purpose of transit.">>
You don't have to explain. ;-)
Many people find Geneva to be a beautiful town. Before I retired, my job in the USA required me to go to Geneva a few times every year. We all have to suffer sometime. ;-)
On weekends, or at the end of a trip, I always got on a train and went somewhere else in Switzerland. I wanted to see the beautiful places, or hike in the countryside, not stay in a city. In recent years, I have gone back with a friend, and having a local citizen show me some of the nice things about the city has made it more enjoyable and interesting. But, if I were in Geneva, I'd still take a train somewhere else. Just my opinion. ;-)
<<"Sorry, what I meant is Rigi Cogwheel train. I want to have experience riding Rigi Cogwheel :) . If it is not possible to visit Entlebuch at the first day, would it be possible to visit Rigi or Pilatus mountain on the day 1? (with assumption we can manage the jetlag)">>
It is definitely possible. Many people squeeze in both on the same day, but it requires careful planning, an early start, and sticking to a tight schedule. I would only do one, and if i were not to tired, I would spend some time in the old city of Luzern and see some of the famous sights.
There are various routes to go up on the Rigi. It is a "gentle" mountain. Pilatus is "harsh."
If you choose to take the boat to Vitznau in order to take that particular route option to go up on the Rigi via the cograil from Vitznau, you might even get a nap on the boat. ;-)
The Pilatus cograil is a much more exciting experience.
I have attached a couple of very old photos of the Pilatus Cograil. The cograils ones that go up the Rigi from Vitznau or Arth Goldau are much calmer. ;-)
I am still puzzled about your interest in the Entlebuch region. It is a region of forest, farms and mountains (but not high Alps) and, unless you plan some fairly serious hiking, there is not much to see that compares with the mountains near Luzern.
For my own curiosity, since I often go through there when I take the mountain pass route from Sarnen to the village of Entlebuch, on my way to the Emmental, would you mind telling me what have you found (or where have you found information) that interests you. I'd like to take a look on one of my trips.
The Kneip Path Fluhli is in Schaffhausen, which is north of of Zürich, quite some distance from Luzern.
I cannot find link for the "Naked Mountain" except for a stark photograph taken near St. Moritz:
Please make sure that you look at your journey(s) on a map to get a sense of the geography, and use the time table to estimate travel times:
I sense that your knowledge of Swiss geography might need a little fine tuning. ;-)