Zurich

Go to Luzern rather than Zurich. 3 day would be perfect.

I liked Zurich. We took the bus to the Lindt chocolate factory, took a boat ride on the lake, did a City tour about the history of Zurich that took us down below the current street level and we had some great dinners. Also, the grand kids got to visit the FIFA Football soccer) Museum which they really enjoyed. I thought it was a great couple of days for getting over the jet lag coming from the West coast.

Depends on your travel history...interests and future plans in and around Switzerland.

We've had the opportunity to visit Switzerland more than once...and we've found Zurich to be a City rewarding to stay in.

IF you decide to stay in Zurich my recommended section is the "Old Town" along the river and Lake.
Zurich airport is good and offers easy connections to downtown. Connections from Zurich to Salzburg are good.

IF Zurich isn't your "cup of tea" this trip you have numerous options from the Zurich airport to other parts of Switzerland for your 2 or 3 days prior to your tour starting.

You might look at the Switzerland travel web-site...I find it very useful and informative.

Happy travels!

Zurich is OK, but it is a big business-oriented city that feels like any other big city. You hardly know you are in Switzerland. But Luzern, one hour away by train, is a charming small city that is also on a beautiful lake, with mountains. all around (on 2 sides anyway) and a charming Oldtown area. You can spend a nice day doing an excursion by boat and cogwheel rail to a nearby mountain with views like this:

https://www.rigi.ch/en

https://www.luzern.com/en/

Since you have two or three days, you could compromise. If you are arriving in Zurich, spend your first day there to unwind by walking through the Old Town or along the lake. Perhaps take a short cruise on the lake. On the second day, go to Lucerne (or Luzern). It's a one-hour direct train ride. One full day should be sufficient to see this very compact town and, if the weather is good, ascend to Mt. Pilatus. For the third day, you could stay in Lucerne and perhaps try for Mt. Pilatus if this wasn't done the day before or take a lake steamer. Alternatively, you could return to Zurich and do more exploring, perhaps visiting the cathedrals, tour a chocolate factory, or, if raining, visit the Swiss National Museum. My personal choice would be one day in Zurich and two days in Lucerne. Unlike many others, I actually like Zurich, marvel that such a relatively large city can be so clean and environmentally friendly, and therefore wouldn't want to miss it completely. But I concur that there is more to do in Lucerne.

Zurich is about 50 mins away from Lucerne. If you find good cheap accommodation in Zurich just stay there....

I think the point here is that people generally do not go to Switzerland to experience big cosmopolitan cities like Zurich, of which Europe has many. They go to Switzerland to experience the Alps. That 50 minute train ride south of Zurich puts you in Luzern, on the door step to these Alps. Right on the outskirts is the tall Mt Pilatus, with trains and cable cars to the top. From Luzern a large lake penetrates into these Alps, and there is hourly boat service that will take you there. Another 45 minute train ride south of Luzern takes you right into the high Alps at Engelberg, with Mt Titlis and its rotating cable car to the top.

So while Zurich is a nice city, one of the most livable in the world according to the click bait articles, there are better places to experience what Switzerland has to offer.

The Kunsthaus is a world-class art gallery with a particularly strong collection of Giacometti.

Food is often very expensive, even by Swiss standards.