A Temple with a View at Ulu-watu, Bali
One of the best places to watch the sun set is from the cliffs of Pura Uluwatu, or the site of the old Ulu-watu temple on the island of Bali. The dramatic cliffs overlook the ocean, and arriving before sunset allows you to explore the grounds before the sun begins to go down. The temple grounds are inhabited by a large number of monkeys, which are fun to watch but can be aggressive, so avoid wearing sunglasses or jewelry and bringing food, and be careful with your camera.
Expect to wear a provided sarong over your pants/skirt/shorts, which is a sign of respect at religious sites in Indonesia (true here for men and women). At one end of Ulu-watu is the place where the rhythmic kecak dance is performed every day at sunset, so you can stay for that, but expect it to be crowded.
Ulu-watu is easily reached by car from most places on the southern part of the island. Drivers can be hired from hotels or villas.