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.
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.
Basel is a city on the River Rhine, bordering France and Germany. It is Switzerland's third-most-populous city and home of the pharmaceutical industry. Basel is commonly considered to be the cultural capital of Switzerland with a variety of museums and the zoo.
Interlaken is located in the heart of the Bernese Alps Interlaken is very well visited by tourists. And with good reason. The vicinity to the mountains, the abundance of activities, the unique location between Lake Thun and Lake Brienz and the excellent shopping make this a place well worth visiting. From here it is a short trip to Grindelwald or Lauterbrunnen for more scenery, waterfalls and the Jungfraujoch.
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.