East of the Sydney Opera House is Farm Cove, surrounded by the Royal Botanic Gardens which were established in 1816. The Royal Botanic Gardens host a tropical plant display inside the Pyramid greenhouses, and also marks the site of the colony's first vegetable patch. From the Royal Botanic Gardens you can wander around Farm Cove towards Mrs Macquaries Point. Here you will find the famous Mrs Macquaries Chair which offers fabulous views across the Sydney Harbour, Sydney Harbour Bridge and the Sydney Opera House. The Royal Botanic Gardens also features a wonderful Open Air Cinema over the summer.
East of Macquarie Street is the Domain, a large grass area perfect for getting away from the city, cycling, rollerblading and even just relaxing with a picnic. The Domain is the place to go in December and January with a whole host of live performances, concerts and music. There are also a number of historic buildings along Macquarie Street worth visiting.
The first racetrack and cricket pitch is in Hyde Park, east of the city centre and just south of the Domain. A giant chessboard is set amongst trees and fountains, along with Anzac Memorial. To the west of the park is the Great Synagogue which you can tour around, and the wonderful State Theatre which offers fabulous interior design.
You will also find the 305 metre high AMP Tower Centrepoint. You should definitely take a look at the remarkable views from the tallest observation tower in the Southern Hemisphere.
To the east of the park is St Mary's Cathedral which has a remarkable flooring within the crypt which offers tours around the Cathedral, and the Australian Museum which hosts a number of informative displays on the history of Australia. You will also come across the small Cook and Phillip Park which opened recently in 1999. Along with its attractive gardens, there is also a fitness centre and swimming pool within the park.
The largest park in Sydney is Centennial Park, offering plenty of activities from running and cycling to horse riding. Around the park you can hire horses, as well as bikes on Clovelly Road, and inline skates on Oxford Street. If you'd prefer to relax you can sit around the duck ponds, or cook at one of the barbie sites. During the summer Centennial Park also hosts the Moonlight Cinema.
Various sport areas, a golf course, the Fox Film Studio and Entertainment Complex, Sydney Football Stadium and Sydney Cricket Ground can be found in Moore Park, to the West of Centennial Park. For fishing visit Pyrmont Point Park, bushland visit Davidson Park and walks visit the Lane Cove National Park.