Must see/do in Switzerland in October

My husband and I are going to Switzerland for 7 days in October (end of month). We plan to have our home base in Lauterbrunnen for 4 days (this is set) and maybe staying in Lucerne for 2 days and exploring Zurich for 1 day.

What is a must see/must do? I am struggling with our itinerary considering weather factors and things shutting down. I want to be realistic but still make the most of our time. We would love to hike to different viewpoints as long as it’s moderate, see waterfalls, also open to other activities and excursions. We just don’t know what will be open at that time.

Do you also recommend taking the train for transportation or renting a car? Any instruction here is incredibly helpful!!

For context, this is for our honeymoon. We prefer to explore than relax during this time so we’d love to know what is really worth our time!