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 is more heavily populated, and represents 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.
- Papiliorama. A small zoo featuring an indoor butterfly habitat, and bird and monkey habitats simulating the jungles of Belize both during the day and at night. Kids love it, and parents too, though the extensive playground might take more parental energy than one wants to expend when travelling.
- Visit Boveresse, Val-de-Travers, near Fleurier, for the Absinthe Festival in June
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.