Answer by taking a quote from the following article:

Captain James Cook  (7 November 1728 - 14 February 1779) was a British explorer, navigator, cartographer, and captain in the Royal Navy. Cook made detailed maps of Newfoundland prior to making three voyages to the Pacific Ocean, during which he achieved the first recorded European contact with the eastern coastline of Australia and the Hawaiian Islands, and the first recorded circumnavigation of New Zealand. Cook joined the British merchant navy as a teenager and joined the Royal Navy in 1755. He saw action in the Seven Years' War, and subsequently surveyed and mapped much of the entrance to the Saint Lawrence River during the siege of Quebec.

In 1766, the Admiralty engaged Cook to command a scientific voyage to the Pacific Ocean. The purpose of the voyage was to observe and record the transit of Venus across the Sun for the benefit of a Royal Society inquiry into a means of determining longitude. Cook, at the age of 39, was promoted to lieutenant to grant him sufficient status to take the command. For its part the Royal Society agreed that Cook would receive a one hundred guinea gratuity in addition to his Naval pay.  The expedition sailed aboard HMS Endeavour, departing England on 26 August 1768. Cook and his crew rounded Cape Horn and continued westward across the Pacific to arrive at Tahiti on 13 April 1769, where the observations of the Venus Transit were made. However, the result of the observations was not as conclusive or accurate as had been hoped. Once the observations were completed, Cook opened the sealed orders which were additional instructions from the Admiralty for the second part of his voyage: to search the south Pacific for signs of the postulated rich southern continent of Terra Australis. Cook then sailed to New Zealand and mapped the complete coastline, making only some minor errors. He then voyaged west, reaching the south-eastern coast of Australia on 19 April 1770, and in doing so his expedition became the first recorded Europeans to have encountered its eastern coastline.  On 23 April he made his first recorded direct observation of indigenous Australians at Brush Island near Bawley Point, noting in his journal: "...and were so near the Shore as to distinguish several people upon the Sea beach they appear'd to be of a very dark or black Colour but whether this was the real colour of their skins or the C[l]othes they might have on I know not." On 29 April Cook and crew made their first landfall on the mainland of the continent at a place now known as the Kurnell Peninsula. Cook originally christened the area as "Stingray Bay", but later he crossed this out and named it "Botany Bay" after the unique specimens retrieved by the botanists Joseph Banks and Daniel Solander. It is here that James Cook made first contact with an aboriginal tribe known as the Gweagal.  After his departure from Botany Bay he continued northwards. He stopped at Bustard Bay (now known as Seventeen Seventy or 1770) at 8 o'clock on 23 May 1770. On 24 May Cook and Banks and others went ashore. Continuing north, on 11 June a mishap occurred when HMS Endeavour ran aground on a shoal of the Great Barrier Reef, and then "nursed into a river mouth on 18 June 1770". The ship was badly damaged and his voyage was delayed almost seven weeks while repairs were carried out on the beach (near the docks of modern Cooktown, Queensland, at the mouth of the Endeavour River). The voyage then continued, sailing through Torres Strait and on 22 August Cook landed on Possession Island, where he claimed the entire coastline that he had just explored as British territory. He returned to England via Batavia (modern Jakarta, Indonesia), where many in his crew succumbed to malaria, and then the Cape of Good Hope, arriving at the island of Saint Helena on 12 July 1771.

Which beach did he land on while the ship was being repaired [we can go to $3 ok]?
11 June a mishap occurred when HMS Endeavour ran aground on a shoal of the Great Barrier Reef, and then "nursed into a river mouth on