I lived in Switzerland for 7.5 years. It is a beautiful, amazing place. But lots of rules.
On Sundays, everything is closed. The only shops you'll find open on Sundays are at train stations (except for a couple of small corner shops here and there).
Many shops will not take credit or debit cards with a Visa/Mastercard logo, be sure to have cash in hand (they use the Swiss Franc). Everything costs, very little is free, including museums.
In Zurich, there's a boat that you can use a bus ticket to board, and it takes you along the long end of the lake. It is beautiful, and a peaceful ride. If the weather is right, you'll see the Alps over the lake.
I lived in Basel most of my time there, and I'm a bit partial to it. A small, beautiful and really nice city. If you stay in a hotel in Basel, you'll get a free transport pass for the duration of your stay. You're also right on the borders of France and Germany, and a quick train ride will take you to Colmar France, one of the most beautiful towns I've been to.
For an amazing, although expensive and all-day trip, take the train up to Jungfraujoch. The highest train station in Europe, and you can go out and stand on the glacier and take in the amazing views. You go through Interlaken to get there, so you could start from Interlaken.
Luzern is another beautiful city, and the wooden bridge over the river is really gorgeous.
The most important thing to know if you'll be in the German speaking part is "Sprechen Sie Englisch?" (spreken zie eanglish) - you'll find the Swiss are much more open to speaking English with you if you ask first in German. Same with French - I can't spell it properly, but "Parles-vou Anglais, si vou plais?".
Enjoy the beautiful country I first adopted as my home after leaving America!