a few days iin switzerland

Paul, Bern, which is almost in the middle of Switzerland, is just a few degrees lattitude north of Minneapolis. That can give you an idea of what you may encounter in Switzerland in November. As for hiking, mountain trails will be snowed-in. So you will need to do your hiking at lower elevations. As for cities, I personally really like Lucerne. Zurich will give you a big city experience (think Minneapolis minus the skyscrapers), Lucerne a small city experience (think Duluth). But staying with friends in Zurich could be a big plus as they could show you around. You won't make a mistake visiting any of the Swiss cities. Each is distinctive--Geneva is French; Zurich (along with Lucerne) is Germanic; Lugano is Italian. You'll find good restaurants in any of the cities. If you go to Rome, keep in mind the travel time. Venice, Florence, or Bologna might be better possibilities. Are you traveling open jaw--into one city and out another? Enjoy Brussels--great restaurants and chocolate there!

Sorry to say, November is not a good time for hiking in Switzerland. November is the time when conditions are too wet and cold for hiking but not cold enough for skiing. The weather can be quite foggy and wet, with frequent snow/rain mixtures. It won't be terribly cold at lower elevations (despite the higher latitude of Europe compared to most of the US, much of western Europe has a much more mild climate than you would otherwise expect, due to the moderating influence of the Gulf Stream), but not great for spending time outdoors. You may want to stay in one of the cities and take a daytrip to see the Alps.

Many posters on this site will automatically steer you towards the Berner Oberland. But in November, this area can be an expensive, rain and fog-soaked ghost town.