Zermatt
Zermatt is a good place to start many hikes into the surrounding mountains, such as the Haute Route that ultimately leads to Chamonix in France.  A complex of cable cars and chair lifts carry skiers in the winter and hikers in the summer; the highest of them leads to the Klein Matterhorn, a small outcropping on the ridge between Breithorn and Matterhorn that offers cool views in all directions. It is possible to cross into Italy via the Cervinia cable car station.