Geneva is probably the most international city in Switzerland: several global organisations (e.g. United Nations, World Trade Organisation & Red Cross) and corporations have their head quarters here. For tourists the Jet d´Eau ("water fountain"), the many quality watch stores, the large Lake and the vicinity to France are most obvious.
Most international visitors will make a stop in Luzern. The city offers the old Kapellbrücke as well as old buildings, murals, houses, souvenirs shops, a stone lion and lots more. Just around the corner are the Vierwaldtstättersee (aka Lake Lucerne) and the mountains with Rigi, Pilatus and Titlis the best known.
Montreux is located at the east end of Lake Geneva and just West of the Bernese Alps. Chillon Castle and Charles Chaplin's museum can be found here. Once a year there is the world famous jazz festival. Yes, there is lots to do.
St. Moritz is known for the Olympic games, the movies that it appeared in and the international jet-set that lives here. This is an exclusive and expensive place! There is some special fun here in winter: alpine skiing, walking and the horse race over the lake. St. Moritz is part of the Graubünden area, where people speak "Romantsch", the 4th official language of Switzerland.
Very few cars are allowed in this village in the Swiss Valais-region. Only for the better! It is nice to stroll and admire the buildings or have a drink. Worldfamous - ofcourse - is Zermatt´s house mountain: the Matterhorn. Indeed it is picturesque. You can view it safely from the Gornergratt or climb it with a guide, but be aware that others tried as well and some ended up in the local grave yard....
Zürich is the financial capital and largest city of Switzerland. You'll find the head quarters of major banks, insurances etc here. Tourists may like the old city, the lake and summer festivals. The "Gold Coast" hosts several international celebrities.