Visit the volcanic caldera in the center of the island. Take a dip in a hot spring along the north coast. Go diving at Pulau Menjangan.
Part of largely Muslim Indonesia, Bali is a pocket of Hindu religion and culture. Renowned for art, dance, music, food, great surf, and beautiful diving, Bali is a wonderful destination with something for everyone. Though heavily traveled, it is still easy to find some peace and quiet if you like.
Balinese is linguistically distinct from Bahasa Indonesia (although the Indonesian lingua franca is widely understood). English and many other foreign languages are widely spoken.
Most visitors will arrive at Denpasar International airport. Taxis are available at the airport, but most hotels will send a car to pick you up-- even from as far as Ubud.
Taxis and bemos (minivans which serve as a flexible bus service) will get you almost anywhere for day trips. Intercity buses are also available. Car and motorbike rental is available, but may not be safe for drivers used to more formal traffic rules. Consider hiring a car and driver as you can relax, be safe, and not get lost.
Bali has a huge variety of cafes and restaurants.
Despite the terrorist bombings, Bali remains an appealing destination, perhaps even more so because the trajic events have reduced the number of tourists. It seems that no area of the world is immune from terrorist activity, and there is no real reason to think that Bali is less safe than Madrid, New York or London. Having said that, it would certainly be prudent to avoid high profile western hang-outs anywhere in Indonesia, and of course beware of pick-pockets, money exchange scams and all of the usual annoyances.