Help! I don't know where to start!

In 1986, before Rick Steves became famous, my ex-wife and I met with him for several hours to plan our Europe trip. Among other things, he recommended Walther's, in Gimmelwald, a little town up in the Hills above Interlaken. We spent 3 days there, I believe, and it was quite literally the closest thing to heaven I have or am going to experience in this lifetime.

Spend one day taking the train up to the Jungfrau on the far side of the valley, and one day starting by taking the cable car up to the restaurant with the 360 degree view of the alpine mountains, have breakfast, and go for a nice long ramble. And one night having a coffee with schnapps sitting outside looking up at the best view of the Milky Way you are likely ever to get.

I believe this is still covered in his books, at least the last time I looked (which was admittedly a while ago). One of my daughters visited a few years ago, and liked it as much as I did.

Jungfraujoch and Schilthorn (mentioned above) won't be great options for someone on a tight budget (around $500 USD for those 2 rides), but Gimmelwald is lovely and a great place for hiking, which you can do with minimal expensive cable car rides if you have the physical fitness.

Where will you be going after your 3 days in Switzerand? That could affect the answer.

I am following this, in the same boat. The only thing I have for sure is getting to St. Moritz from Zurich, staying in a small town near there (Sils Maria), then taking the Glacier Express to Zermatt. That leaves me with 4 days left to fill. I prefer staying away from touristy towns and would rather experience more authentic Swiss culture. My husband is limited in how far he can walk, so hiking is not in the picture for us. ChatGPT was great for itinerary if you don't mind being on the same itinerary as it seems everyone else is on (who also presumably used a LLM for planning). So would prefer recommendations from real intelligence instead.

If you want car free mountain villages near Zermatt that are less touristy - Bettmeralp or Saas Fee.

Yes, rather than trying to eat the whole smorgasbord in one sitting, pick one particularly scrumptious item and savor it thoroughly.

wanderweg mentioned Saas Fee, on nobody's radar except certain cognoscenti. Can only be accessed by post bus (if in a car, you must park in the huge parking garage entering town). Over shadowed by nearby (as the crow flies) Zermatt.

A different type of experience would be Luzern for 3 days. Ride lake boats, several mountain top experiences, (Pilatus, Rigi, Stanserhorn), plus city.

You could base yourself in Interlaken and just wander the nearby valleys; the hikes are insane but you don’t need hardcore gear, and the little villages are super cute to poke around.

As a student, I assume you are comfortable with hostels. If so, the answer for you is Gimmelwald, Gimmelwald, Gimmelwald. Incredible hiking and seemingly infinite vistas. And if you can get a room at Mountain Hostel, certainly affordable.