Here's an ideal itinerary for 7 days in Sydney:

Day 1: Arrival and Exploration

• Arrive in Sydney and check into your hotel
• Take a stroll around the iconic Sydney Opera House and Harbour Bridge
• Visit the Royal Botanic Garden and enjoy the stunning views of the harbour
• Head to The Rocks, a historic area with cobblestone streets, boutique shops, and restaurants

Day 2: Beach Day

• Head to Bondi Beach, one of the most famous beaches in Sydney
• Take a surf lesson or simply relax on the beach
• Walk along the Bondi to Coogee Coastal Walk, a scenic 6 km trail with stunning views of the ocean
• Enjoy dinner at one of the many beachside restaurants in Bondi

Day 3: City Sights

• Visit the Sydney Tower Eye, the tallest building in Sydney, for panoramic views of the city
• Explore the Art Gallery of New South Wales, which houses an impressive collection of Australian and international art
• Take a ferry to Taronga Zoo, where you can see a variety of animals and enjoy stunning views of the harbour
• End the day with a sunset cocktail at the Opera Bar, located right on the harbour

Day 4: Day Trip to Blue Mountains

• Take a day trip to the Blue Mountains, a stunning natural wonder located just outside of Sydney
• Visit the Three Sisters rock formation and take a scenic cable car ride
• Explore the charming town of Katoomba and enjoy lunch at one of the local cafes
• Return to Sydney in the evening and enjoy dinner at one of the city's many restaurants

Day 5: Food and Wine

• Take a food and wine tour of the Hunter Valley, one of Australia's premier wine regions
• Visit several wineries and sample some of the region's best wines
• Enjoy a gourmet lunch at one of the wineries
• Return to Sydney in the evening and enjoy dinner at one of the city's many restaurants

Day 6: Cultural Experience

• Visit the Australian Museum, which showcases the country's natural and cultural history
• Explore the vibrant neighbourhood of Newtown, known for its street art, boutique shops, and restaurants
• Attend a performance at the Sydney Opera House, one of the world's most iconic performing arts venues
• End the day with a drink at one of the city's many rooftop bars

Day 7: Relaxation and Departure

• Spend the day relaxing at one of Sydney's many beaches or parks
• Enjoy a leisurely brunch at one of the city's many cafes
• Depart Sydney in the afternoon, feeling refreshed and rejuvenated after a week of exploring this beautiful city.