The Malcolm Douglas Crocodile Park and Wildlife Refuge looks like something I would really enjoy! They have daily feeding displays and boast some of the largest crocodiles in Australia. Approximately a 10-15 minute drive from the Pearle Resort. $30 concession entry.
Greg runs a Broome Astronomy Experience in which you can view the stars and planetary systems through their binoculars and high powered telescopes. It is approximately 15 minutes out of Broome. $65 per person, or $85per person with taxi transfers.