Hello again Carole Ann,
Back on May 21 I mentioned that I would get back with my thoughts about staying in one place for the entire month, so here goes.
First, I should say that I totally understand your desire to not be living out of your suitcase. Going to a new place every night and having to lug a suitcase and check in for each move is not what I would want to do. Second, I suppose I should ask if you have already booked your accommodations in Berne ? If your answer to this question is "yes" and there is no way to change this, then that is it, I guess, and I hope you enjoy your travels each day away from and then returning to Berne for the night. If, on the other hand, your answer is "no", or if there is any way to change this, I was wondering if you might consider having three or four bases (say one per week) to cut down on what will be repetitive train travel time. I would suggest staying up to one week in some place in the Ticino, one week in the French-speaking part of the country (called Romandie), and two weeks in two different places in the German speaking part. I read earlier in this thread that one can go by train from Geneva to St. Gallen in 4 hours. Well, that is 8 hours if you return in the same day. That's fine if you are on a business trip, but for a tourist, it doesn't leave much time at the other end. But you are not thinking about Geneva, you are thinking about Berne. I checked the schedules and find that even from Berne to St. Gallen, you are looking at about 3 hours one-way, so you'd spend 6 hours on such a day trip. You can't do justice to north-eastern Switzerland in one day, or even two or three, so the number of hours going back and forth on the train begins to add up. I'm kind of afraid that as you pass through Zurich Hauptbahnhof for the umpteenth time, you will start to feel more and more like one of the almost half million people (466,800 in 2016) who board or alight in this station every working day. Berne is the second busiest station in Switzerland, with 210,000 (in 2016).
So what bases would I suggest ? I would suggest Lugano for the Ticino portion. It is a short trip to Italy from there. I don't know where you were thinking of visiting in Italy, but if it was Milano you could get there quickly from Lugano, much more quickly than from Berne. For Romandie I would suggest Montreux, as this would make Geneva, Lausanne, Gruyères (just to name a few places) and the canton du Valais easy to get to. You could even make Berne your location for exploring Romandie as it is not far from Lausanne and actually closer to places like Morat, Fribourg, Neuchâtel, and the Bielersee than is Montreux. Berne is also in easy striking distance of Interlaken and the Lauterbrunnen area. For the other two weeks, why not choose some place near Lucerne and another place up in the north-east (perhaps St. Gallen). I don't know where you are thinking of going to in Germany, and that might affect where I would suggest for the two weeks in the German-speaking part of Switzerland.
The other day I posted an animation of passenger traffic and from this you can see the major hubs (with Zurich at the top) and others. These hubs are also where you will find the most daily connections to do your explorations of Switzerland. You will probably want to spend your overnights fairly close to these hubs.
By the way, in closing, I should say that I almost never try to dissuade a person from where they want to go or what they want to see (I can't remember how many times I have read less than positive comments about the Rheinfall) but I just thought I would pass along my thoughts. I have already mentioned la Fête des Vignerons and if you are looking for any ideas about what else I think might be interesting in any of the areas I have mentioned, I'd be happy to do so. I should admit that I probably do over-emphasize the French-speaking part of Switzerland. I do notice that Snowman has mentioned a few places I like. Indeed there is no public transport to the Creux du Van but one can take the train to Noiraigue (see attached map) and there are two walking routes up from there. If you have a car, you can drive up from Bevaix, park at La Grand Vy, and it is a very short walk from there. You can eat and even stay over at La Grand Vy.