Mrs. Macquarie's Road, Sydney, Australia
Once an Aboriginal sacred site, the gardens were unsuccessfully used as a government farm in 1788, and founded as the Royal Botanic Gardens in 1816. That's a long time ago, before Dick Clark was born, before Barbara Stanwyck began her career, and before I bought my last pair of running shoes.
The Gardens is a 74-acre/30 hectare expanse of gorgeous grounds where only walking is allowed (no bikes, etc). Sections include an herb garden, palm garden, tropical centre, rose garden, bat colony, oriental garden, and fernery. There are a LOT of fox bats that like to nest there, and because they destroy the trees in which they choose to nest, the Gardens uses unnamed methods to discourage this. It's freaky, though - all of those huge bats hanging from a stark naked tree.
There are several entrances into the Gardens, including one right in front of the Opera House. You can walk up to Mrs. Macquarie's chair and look at the harbour scenery (incuding the bridge, opera house, and city), then head back towards the city center. The Government House, which is no longer the official residence for the Governor, is on the Gardens and open for tours. There is also at least one place to have a decent lunch, near the government house.
There are free guided tours daily at 10:30. The park is open from 6:30 A.M. to sunset. It's a good place to run in the morning. Or so I hear.