The voyage then went to Tahiti ( where the transit of Venus was observed , the purpose of the mission ) , to New Zealand and to the east coast of Australia , where Cook mapped the coastline and made landfall at Botany Bay and at Endeavour River ( near modern Cooktown ) in Queensland , where they spent seven weeks ashore while the ship was repaired after damage on the Great Barrier Reef . The voyage then progressed to Tahiti ( where the transit of Venus was observed , the overt purpose of the mission ) , to New Zealand and to the east coast of Australia , where Cook mapped the coastline and made landfall at Botany Bay and at Endeavour River ( near modern Cooktown ) in Queensland , where they spent almost seven weeks ashore while the ship was repaired after foundering on the Great Barrier Reef .