Amuk Bay East Bali
Amuk Bay in East Bali includes the coastal towns of Candi Dasa and Padangbai (‘padang‘ is Balinese for grass, ‘bai‘ is Dutch for bay). The name of the bay is famous after the term ‘ running amok. When Balinese wanted to commit suicide, they would (as usual) bottle their emotions, then explode in anger, running around attacking anyone in sight, knowing they would be put to death by the other locals (love civilization don’t you!). The expression spread around the English speaking world, but this is the birthplace.
As any visitor to the area can tell you things are slow, but if you want a mellow place to relax, that is on the coast and within 2 hours of Kuta, Amuk Bay will work. PlanetMole features an article about a tourist submarine that is in operation there, one of only 2 in the world. Sounds interesting.