South of Lucerne: Mount Pilatus.
Start in Hergiswill, take the train to Alpnachstadt (10 mins), from there, take the cogwheel train to mount Pilatus, the steepest cogwheel train in the world (48% gradient). Go up to the top of Mount Pilatus (2106m). Proper restaurant there. You can hike from there, or do a tour on foot. Or, you take the cable car down to Kiens/Lucerne. Awesome views. From there, take the bus to the shores of the lake (Chapel Bridge). Take the (classic) ferry back to Hergiswill. This will take you a whole day. (We stayed in Hergiswill for two nights on our way to Italy - In hindsight a good starting point for the daytrip: parking in Alpnachstadt is expensive; in Hergiswill it was f.o.c.
It's incredible to use so many types of transport in one day. And to absorb so many views within a 10km radius from where you started.
And, as you can imagine, everything goes like a Swiss watch, is well-maintained etc. Fun thing is: when we didi this in 2015, we were able to di this day with only one ticket from the Swiss Railroad Company. But, as usual: Swiss tickets etc are eyewatering expensive.
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