So I can offer a bit of insight on Switzerland as I was there for about 3 months. It may help a bit to know what exactly you're interested in seeing in CH. As others have already stated, best way to get around Switzerland is by train. They go to all of the major cities and also pretty much all of the picturesque towns.
I would honestly say that Swiss cities are on the whole not all that fascinating. Bern and Lausanne are nice. Zurich is the largest city and probably has the most going on in the way of nightlife. I'd really recommend spending a few days hiking though if that's your thing. Switzerland is truly one of the most beautiful countries in the world. The backdrops to the cities are nice, but actually being in the mountains is another thing entirely.
For some idea on day hikes, check out this page on the
Via Alpina, which is an extended hiking trail crossing the Alps from east to west. I think the whole thing is like 370 km but it's split into 20 or so "stages," which can easily be done as day hikes. Between each stage is a town with (AFAIK) a train station, accomodation, food, etc. So you can (1) do a day hike from one town to the next and just take a train back to whatever city you're staying in or (2) do a day hike from one town and turn around half way or so back to the town you started from (a good option if you're not sure you can finish the hike). Some of the segments I did were Grindelwald --> Lauterbrunnen and Griesalp --> Kandersteg, both of which were incredible.
If you're not that into hiking, I would say still check out Interlaken and Grindelwald, the former being a large tourist town (with activities like skydiving and paragliding if that interests you) and the latter being a much smaller but still very well-known town. These are both around central Switzerland and somewhat close to Bern (1-1.5 hr train ride away). Zuerich is further north towards the border with Germany. Lucerne is halfway between Bern and Zuerich and supposed to be very nice, but I've never been so maybe someone else can advise you.
In the southwest closer to the French-speaking section and on the border with Italy is the town of Zermatt, which you'll probably know if you google pictures of it since it's where the Matterhorn is. Plenty of easy day hikes to do here and also many tourists in town.
I really don't know anything about the Italian part of CH so best leave that to google or someone here who actually knows about that.
So that's pretty much all I can think of...sorry for the terrible organization -- I was just writing as the thoughts hit me.
And there aren't really any faux pas that are particular to Switzerland. Maybe just be aware that there are four national languages (Swiss German, French, Italian, and Romansch (spoken by a very small minority)). Often times, people from different sections of the country (especially younger people) will communicate with each other via English. I noticed there was some casual rivalry between the French and German regions. If you can speak decent French or German, then definitely try to use it when you can in those respective regions, but French in the German region and vice versa will definitely get you a few looks.
Enjoy your trip! I'll actually be back in Switzerland next summer to do all of the Via Alpina :D
Feel free to message me if you want more details or have any questions!