See all Things to do in Wollongong Wollongong for: Adventure, Food And Dining, Art And Culture, Nightlife, Spa, History, First Timers, Family, Romance, Shopping Cockatoo Run Phone: 1300 65 3801 About Cockatoo Run, (toll free: 1300 65 3801), [18]. Sundays. The Cockatoo Run is a vintage train that climbs through the Morton National Park Rainforest to Robertson and Moss Vale. Add to Wish List