now for what you should do...>French region:
- Nyon is a pretty town with a nice Castle
- Chateaux Chillon is stunning, a must go (Take the boat from Vevey if possible)
- Neuchâtel is pretty too>German region:
- Fribourg is nice
- The area around the Thunersee is a MUST SEE, specifically Thun, Spiez, Interlaken.. go up a few mountains like the Schilthorn, Niesen, Jungfrau. Dont miss Oberhofen castle, take the boat to that and around the whole Thunersee while your at it.. This area of the Berner Oberland is my home and I definitely recommend it!
- Luzern/Lucerne as >>1311107
said is stunning, on of the best cities in Switzerland and Europe, literally amazing! Go across the Kapelbrücke and explore the Altstadt
- Schaffhausen is stunning too where you can also see the famous waterfalls
- St Gallen like Luzern is one of the most stunning places in Europe, the Altstadt is a gem and the Abbey of St Gaul is listed on UNESCO I think also if you are adventurous or have time you can visit the Principality of Liechtenstein for a day (just to say you have)>Italian region (really recommend)
- Lugano, known as the Swiss rivera..
- Bellinzona for the Castles which are amazing
- May as well do a quick trip to Lake Como since your close