I've never done this but it's highly recommended.
Bali Bird Walks with Victor Mason: http://www.balibirdwalk.com/index.html

As far as cultural tours, you'll be spoiled for choice. I'd suggest that you see what your resort/hotel offers as a starting place. Schedules for dance performances and temple ceremonies are widely posted. You will have no problem going on your own.

(Oops, pressed the button too fast.)I also really like the programs offered by Danu Enterprises. Their tours are inclusive of airfare, but if you contact them you can arrange to join all or part while you are in Bali.

http://www.danutours.com/bali_menu.htm

In Ubud there is the Taro Elephant Park, which you can check out. Elephants are not native to Bali but they have Sumatran elephants. Also just south of Ubud in Sanur there is Bali Safari and Marine Park. In Batubulan on the way to Ubud is the Bali Bird Park.

Also, not in Ubud but in Nusa Penida, an island just south of Bali, is the Friends of the National Parks, which is regenerating the endangered Bali Starling. http://www.fnpf.org/
They also are working on organgutan rescue in Indonesian Borneo (Kalimantan).