3 day Switzerland trip

I would first determine if flying out of Zurich or Geneva works better for you, then pick one place that is most convenient--three nights is a short amount of time and I would not stay more than one place.

Spend all the time in Luzern in one hotel and take day trips is more bang for 3 days. You can only get direct flights to Barcelona from either Zurich or Basel. It is easier to fly from Zurich than Basel the morning of.

If you really want to go to Zermatt, presumably to see the Matterhorn (that is why everybody else goes there in the summer), stay there the whole time. What time is your Barcelona flight? Swiss has several nonstops throughout the day from Zurich Airport. It takes 3 1/2 hours to get from Zermatt to Zurich airport, so the 12:20 flight is the earliest you should book.

There is plenty to keep you busy in Zermatt for 2 1/2 days, and you stand a chance of having a clear day to see the Matterhorn. Take the Gornergratbahn up for the view, and to the Glacier Paradise by cable car to go inside a glacier.

I agree with staying the entire time in Lucerne. The town itself is charming, and great options for day trips. Zermatt is a "one-trick pony" per RS, and I agree. If the summit is all cloudy, your options are limited .
St. Moritz is glitzy with high-end shops that are located everywhere. And many shops are closed in Switzerland on Sundays. You're not really experiencing Switzerland. And with the scenic train ride, you are spending too much time moving about Switzerland, not actually being there.
It's a beautiful country, and Lucerne offers the most options, even if the weather is cloudy, as just being there is so pleasant. Saturdays are market days around the Chapel Bridge, with the best fresh breads, cheese, and yogurts.
Enjoy!

Thank you for the advice. I was also thinking of Interlaken or Chur. Would Lucerne be the best hub, and make short day trips from there?

Is it better to Airbnb in Lucerne or get a hotel? Any recommendations? Also, would it be better to rent a car between the 5 of us or should we stick to trains?

Tell us the family make-up and ages.

Forget the car. You have one of the best rail systems in the world to access.

Ages are 61, 54, 28, 26 and 21.

View some utube videos on Lucerne-
Chapel Bridge, the boat rides on the lake, Mt Rigi, the open air cable car to Mt Stanserhorn , Mt Pilatus, and a bit further, Mt Titlus.
Enjoy!

A couple of ideas. There is a 3-day Tell Pass for 230 CHF per person, which gives unlimited travel on boats, buses, trains, cable cars in the region. https://www.tellpass.ch/tellpass/information/geltunsbereich/dokumente/geltungsbereich/TellPass_Streckennetz_EN_Sommer_2024.pdf

If you stay in a hotel in Luzern, you will get a Guest Card valid on local transport within the city and discounts of 10% to 20% on many of these attractions. https://www.luzern.com/en/information/useful-information/visitor-card-lucerne

I do not believe this is included with airbnb.

Thank you. All these tips will help great!

I would be interested in more tips about places to stay and eat at Lucerne.

Besides the tellpass, is there any other cost saving tips on train tickets ?

Accommodations: Just start looking--it is an expensive place and every day you wait the availability will be less. I use Booking.com--you can plug in your budget and all other needs and see what is actually available.

Rathaus Brauerei Luzern was great.