Day trip from Zurich to Alps

Faye - From Lucern, she can day trip to the alps and visit Kleine Scheidegg, which is 58 km from Lucerne. Mount Titlis and Mount Rigi are other options as well on exploring the alps.

https://www.myswitzerland.com/en-us/experiences/kleine-scheidegg-1/

Another option is from Lucerne to the Brienzer Rothorn.

https://www.interlaken.ch/en/experiences/mountains-panoramas/mountain-excursions/brienzer-rothorn

I vote Titlis.
It is one of 3 mountains you can get up from Luzern (the other two being Rigi and Pilatus).
All 3 have trains or cable car to the top, and all 3 will have snow at the top this time of year. Titlis is the highest, it has a small permanent glacier.

Check out these websites:
Titlis: https://www.titlis.ch/en
Rigi: https://www.rigi.ch/en
Pilatus: https://www.pilatus.ch/en/

That said, why is she even staying in Zürich in the first place? Zürich is well down the list of places tourists go in Switzerland. Better to spend the whole 4 days in Luzern, closer to the mountains.
Or is it perhaps for work and she has 4 free days at the end?

The Brienzer Rothorn Bahn is not running. It has shut for the winter. The next trip to the Brienzer Rothorn will be 6th of June 2020.

And the Brienzer Rothorn and Kleine Scheidegg are a lot further than Luzern.
Brienzer Rothorn is above Brienz, between Luzern and Interlaken.
Kleine Scheidegg is above Wengen, which you rejected as being too far.

Appenzell is also at the foot of a mountain. She could take a train to Wasserauen (11 min.), then cable car to Ebenalp. She may not need to do both mountains, but has options if weather is an issue one day.

I've spent a bit of time in Zurich on a couple trips. Honestly, there is really nothing actually wrong with it, but there are quite a few places in Switzerland that are more charming. Relatively speaking, Zurich is a big city. On the other hand, Luzern is spectacular, as are the available day trips from there. Luzern is only a one hour train ride from Zurich. From Luzern it is easy to get to the top of a mountain. I would choose based on weather. The day we went up to the top of Rigi, Pilatus and Titlus were covered with clouds. The next day Rigi was cloud covered! Bern is not in the mountains, but it would be another nice day trip from Luzern.

Yes, Chris F, this is the end of a business trip. Her colleagues will still be in Zurich finishing up - but her part of the trip will be over. So she doesn't want to leave Zurich and strike out on her own completely. Having been to Switzerland, I just couldn't stand her being there and not going up in the mountains! You have all given me some great options that I will pass on to her. Thank you.

Striking out on her own is exactly what she should do and head for Murren and spend a couple of nights. Yes, don’t get stuck in Zurich if at all possible. There’s really no safer country in which to travel alone. And she won’t be alone as there will be plenty of other people riding the trains on their own.

I agree with the comments about Zurich. It really is charmless--more of a business type city. It has some good restaurants --most are expensive. Once we were there and it was a national holiday--lots of restaurants were closed except the Kronenhalle--one of the most expensive meals we have ever had--it was very good but not our style of dining. We were only there because of flying out. We got a hotel near airport--some decent priced ones near airport.