1. After arriving in Zurich, heading east via Herisau to stop at Appenzell for it's old town/townhall. Then head to the tiny principality of Liechtenstein.
2. Head via the Rhine Valley to ascend the Julian Pass to Switzerlands largest canton, the Grisons & onwards to spend time in St Moritz.
3.. Taking the Bernina Express train from St Moritz over the Alps to Tirano in Italy. Amazing. :)
4. Take a train to Zermatt, the resort beneath the Matterhorn.
5. Lake Geneva Region/Lausanne.
I won't say Berne because anyone who ever thought of imprisoning bears in a small pit for the entertainment of tourists should be put up against a wall & shot though if you can ignore that it is a nice place & you can stop off in Gruyere on route to sample the famous cheese.
6. Interlaken & over Brunig Pass to Lucerne & then back to Zurich. You've just completed a grand tour of Switerland.
Opps that was 6, cheating again. This was the tour I did in 8 days though it headed in & out of Italy twice to the beautiful lakes. However if barr Tirano, you don't want to go back into Italy, it is a good guide to the must sees.
Regarding eating, suppose a cheese fondue is the thing to try.
http://www.tourvacationstogo.com/switzerland_tours.cfm?npid=20216&nhr=1 about 9 years ago
If you are going to Lucerne then may I suggest you visit the following i.e.
1. The Lion's Monument (has very interesting history about it).
2. Take a relaxing scenic fjordlike lake cruise (approx. 1 hour) with the captain making
commentaries on interesting buildings like old castles etc.)
3. Take a cable-car ride to the top of Mt. Titlis (20,000 ft). Ride will take you up with three (3)
types of cable-cars. Their food-court also sells good food. You will not regret it. about 9 years ago
1. The Jungfraujoch is amazing. The train ride is stunning.
2. Zurich is beautiful. Take a dip in the Zugsee. Go up to the top of the Cathedral. The views of the city are lovely.
3. The cable cart at Mount Pilaus near Luscern is a lot of fun. There is an adventure activity park there and the worlds steepest train track. almost 9 years ago
Depends on your time & budget:
I would recommend you:
1. to pay a visit to Lucerne which is the most beautiful swiss city, you can just enjoy having a walk aroud the city or take a boat in the lake
2. to pay a visit to Montreux, go to Chateau de Chillon which is 45min walk from Montreux train station, or go to it by boat. The cruise in Lake Geneva is worth trying as well.
3. to go hiking ANYWHERE as well as cycling, Switzerland is a hiking & cycling heaven
4. Swim at the Aare River in Bern, if it's not too cold, it's a must do really. And have a walk in the old city as well as going to Barengraben & walk up to Rosengarten
5. to go to Lugano, because you cannot miss the diversity of cultures in Switzerland about 8 years ago
And don't forget to take one of these scenic trains.
I also recommend you to go to Kleine Scheidegg instead of Jungfrau which is less touristic ;)...
If you are not a fan of big cities then skip Zurich & Geneva, because small cities are more interesting about 8 years ago