About Bernese Oberland:
This is the mountain chain that contains Eiger, Jungfrau, Mönch etc. It is also home to Europe's biggest continental glacier - the Aletschgletscher. It is best suited for mounaineering, but has many bolted routes - not exactly sport climbing, but rather adventurous multipitch. You can also easily find trad climbs, more or less protectable. In winter, ice climbing scene is also very prominent, especially in such towns as Kandersteg or Adelboden.
Tourists are attracted to it by the Jungfraubahn, the little train that brings you to the top, on the shoulder between Monch and Jungfrau, at 3 500, in around 1h from your car. Good deal that costs you 100 euros one way...
Here is the webcam directed upon the Eiger North Face to give you some feel for the place.
Other mountains, maybe less imposing, but certainly not less beautiful abound in the vicinity. To start with Wetterhorn to the left, and continue with numerous summits inside the Aletch, where most of the time you might need your skis and a lot of adventureous spirit to explore the furthest corners.