We spent 3 nights in Lucerne, and we enjoyed exploring the city, and especially enjoyed a lake cruise on a paddlewheel steamer to Weggis for lunch.
We also spent two nights in Engelberg (1 hour from Lucerne), and went to the top of Mt. Titlis, which my family of five absolutely loved!! We all decided that if we get to return to Switzerland, we want more snowy mountaintop experiences, so we will head to Murren!
I have read so many wonderful things about the Berner Oberland, especially Murren and Wengen. I think between the setting, the ease of hiking, and the spectacular views that it would be an amazing place to stay for a few days.
I agree with the others - take a vote! I am sure there would be a lot to love about either stop. Your approach to decisions was similar to ours for a different trip - we watched the RS Barcelona, San Sebastian, and Madrid videos to let our Spanish learning sons pick which part of Spain to explore last summer.
One bit of food advice - we did go to the Coop stores a few times to pick up snacks and a couple of picnic lunches for our Swiss days. The restaurant menu prices really were as expensive as many say! We also chose hotels that provided hearty breakfasts with the cost of the room - that was a savings for our family as well.
Have a great trip!
Laurie