Some of the best :
* Go up Gunug Batur (1800m) to see the sunrise over a lake and the sea. You will see also the huge crater of Gunung Batur.
* Go up Pura Lempuyang and its 1 700 steps, but you have a nice view at the top.
* Walk across the rice fields around Ubud.
* Walk in the rice field of Tirta Gangga with a local guide that will explain the plants and the way of life of the people far from the tourist center.
* Visit the temples of Bali : Tanah Lot on its rock for sunset, Ulu Watu on the top of cliffs and full with monkeys, the best pickpockets of Bali, Besakih the biggest temple, Tirta ganga and its fresh water swimming pool, Tirta Empul and its sacred water, Goa Lawah and its thousands of bats,… There are thousands of temples on Bali and each one is specific.
* Ubud, the cultural village and its artists, famous also for the view over the terrace rice fields
* Singaraja, former capital of Bali under Dutch control
* Bangli, nice quiet city with beautiful temples
* The Aga, balinese from the origins and from the mountains
Attend one of the numerous ceremony taken place all over the island every day, which give the rhythm to balinese life.
Gunung Kawi, king and queen burials from the 11th century
The list is long. This is just a first glance over what you can do.