Neptune's Grotto is quite fantastic.  It takes 25 minutes to walk down the 654 steps to Neptune's Grotto, and although going up is somewhat strenuous, it's not horrible.  There is an option to arrive there by boat. 

Also, don't forget to check out the Nuoro Museum of Popular Life and Traditions

CoOp Ghivine is a small conservation organisation that is based in Dorgali on the NE of the island. They offer escorted walking trips through the Goroppu gorge at a very reasonable rate ( ) which includes transportation and lunch. Driver-guides take a maximum of around 8 people in landrovers and they have an in-depth knowledge of the geology, flora and fauna of the area and are active conservationists.