You really need three days in Sydney to see the essential city center, while six days would give you time to explore the beaches and inner suburbs. A stay of 10 days would allow trips outside the city and give you time to explore a few of Sydney's lesser-known delights.
Start with an afternoon Harbour Express Cruise for some of the best views of the city. Follow with a tour of The Rocks, the nation's birthplace, and take a sunset walk up onto the Sydney Harbour Bridge. The following day, take a Sydney Explorer tour to the famous Sydney Opera House and relax in the afternoon in the Royal Botanic Gardens and Domain park. On the third day, explore the city center, with another spectacular panorama from the Sydney Tower. Include a walk around Macquarie Street, a living reminder of Sydney's colonial history, and the contrasting experience of futuristic Darling Harbour, with its museums, aquarium, and cafés.
Follow the three-day itinerary, then visit Kings Cross, Darlinghurst, and Paddington on the fourth day. You could continue to Bondi, Australia's most famous beach. The next day, catch the ferry to Manly to visit its beach and the historic Quarantine Station. From here, take an afternoon bus tour to the northern beaches, or return to the city to shop or visit museums and galleries. Options for the last day include a trip to a wildlife or national park, Taronga Zoo, or the Sydney Olympic Park west of the city.
Follow the six-day itinerary and then travel beyond the city by rental car or with an organized tour. Take day trips to the Blue Mountains, Hunter Valley, Ku-ring-gai Chase National Park, the Hawkesbury River, or the historic city of Parramatta to Sydney's west. Or travel on the Bondi & Bays Explorer bus to Vaucluse or the charming harborside village of Watsons Bay. You could take a boat tour to the historic harbor island of Fort Denison, play a round of golf, or just shop or relax on the beach.