Planning 4 nights in Switzerland on our way to Italy. We are scheduled to arrive in Zurich early AM from the U.S. and currently booked for a 4 night stay in Lucerne before we move on to Bellagio. We have been thinking we would want to stay in Lucerne as a base, explore Lucerne, and do a couple of day trips. We are hoping to either take the Gothard Express or recreate that route via a regular ferry and trains. Lauterbrunnen keeps popping up as a great destination although it would be a big day trip via train. It sounds like if we went to Lauterbrunnen, we should just skip the trips to Mt. Pilatus and Mt. Rigi.
With the time limit of 4 days in Switzerland, what is the best use of our time and $$? If Lauterbrunnen is a good idea, would it be enjoyable as a day trip? Would it be better to go directly from Zurich airport to Lauterbrunnen and split our time between that area and Lucerne before moving on to Italy? We like the idea of staying in one hotel for 4 nights but are willing to move if it makes more sense.
Would love input from those who are familiar with these areas of Switzerland. Thank you!