Climb a mountain/volcano, change islands over to Lombok or Gilli's... Snorkelling....
There's a nice big lake in the NE of Bali. Visit Ubud. Visit 3 to 6 or so of Bali's 1,000 temples.
http://www.bali-indonesia.com/attractions/temples.htmHire a car, and do a trip around the island for a few days or a whole week or two....
They have quite a few National Parks too, and cheeky monkey's.
www.wonderfulbali.com/westbali/balibarat.htmOn your drive around Bali, stop off at Medewi for some mellow left handers, west Bali. Plenty of beach break options on the way there too.
There's even a website, things to do in Bali !!
thingstodoinbali.com/So much to do, so little time... go back again next year !
Edit;
One of my best experiences was heading around the island with a mate, and a young local Bali Beach Boy (Ryan), and we had a little Suzuki Jeep, and Ryan could surf, and he directed us to a number of surf beaches.... he took us to his home village to meet his parents and family. We played pool and drank beer in his local pool hall. He showed us the good places to eat.... showed us all kinds of places around Bali.. then when we got back to Kuta, we would hang out with some of the other local guys from the beach, in the back blocks of Kuta, and eat and drink with them. They provide great food, and we come along with some beer to share ! (We paid for Ryan's food and accomm, provided the car and petrol, etc, but we never got lost, and we saw heaps more than we would have on our own.... Ryan was our local tour guide).