Southeast of Zurich, St. Moritz (pop. 5100) is a real paradise for serious hikers and bikers. There are over 75 miles of tracks around the town plus another 200 miles along the valley that were set up for winter nordic skiing. Check out the Val DVina Trail which is chiseled into the mountain side.
To reach this area from Zurich, head southeast on Route A3 and then south on Route A13 to Chur. Turn south on road to St. Moritz for 70km.
Overall, St. Moritz is the 12th most popular hiking trail of all 15 hikes in Switzerland.