Jura Mountains and Fribourg
The Jura mountains cut through five Swiss cantons: Vaud, Neuchatel, Fribourg, Bern, and Jura. The Swiss Tourist Office  lumps the Jura Vaudois in with the Lake Geneva Region which does make sense as odds are if you visit there you'll be sleeping in a lakeside city like Nyon. The northern Jura are more heavily populated, and represent a distinct culture from the rest of French speaking Switzerland.
The cities of the Northern Jura are where the famed Swiss watch making industry took off in the 18th and 19th centuries, and so there are a lot of interesting watch-making related things to see in the region.
Les Paccots  is a mountain resort in the Fribourg Alps in Switzerland.
La Sarraz Castle, located in a small village 20 minutes by train from Lausanne. A recognised site of European Heritage (one of 4 in Switzerland), the current castle dates to the 16th century and stands out as quite unique architecturally unique.
Switzerland is generally very safe. Crime is low and usually limited to towns. If you leave your walet on a table in a cafée, chances are high that it is still there when you get back or it was handed in to the staff. Be aware that the Jura mountains are steep and have some pretty big cliffs. There are spots where hikers and Mountainbikers have to be cautious. While hiking you will get accross the fields where cows are kept. Some hiking routes cross such fields. Usually the cows are no threat, but there where cases where mother cows attaced hikers to protect their young. In case of an accident, Switzerland is very well organised when it comes to rescue services. REGA is an organisation providing rescue by helicopter. They are usually very fast, well equipped and trained, and can be called dialling 1414. Typically they are called for accidents in remote areas, such as the Alps or Jura mountains.
Like all of Switzerland, this region is laced with hiking trails (marked in yellow) and biking trails (marked in vermillion). You can buy first rate hiking and biking maps (about CHF28) at tourist information offices in all towns of any size. For going up into the Jura, a map is strongly recommended; elsewhere you can get by without one.