Hyde Park Barracks is on Macquarie Street, in the heart of Sydney, in a row of colonial buildings that tell the story of the city's beginning. The barracks were designed by Francis Greenway, himself a convicted forger, and built in 1819 to house about six hundred male convicts who worked on government projects, so the man who drew the plans was the same kind of prisoner who would sleep there. Later it served as an immigration depot for women, an asylum and a courthouse, and it now operates as a museum with hammocks and artefacts that bring the convict years to life.
The setting is worth lingering over. Macquarie Street is lined with grand sandstone buildings, including Parliament House, the old Mint and the State Library, and the adjoining Hyde Park offers a shady retreat between avenues of fig trees, with the Archibald Fountain at one end. St Mary's Cathedral stands to the east, and the Royal Botanic Garden and the Opera House are a short walk away. UNESCO recognised the barracks in 2010 as part of the Australian Convict Sites, and the buildings' geometric Georgian lines are a reminder of how rigidly Sydney's early planners thought.
Riding here needs patience. The CBD has tolls, bus lanes, tram works and some of the most expensive parking in the country, and one-way streets make navigation tricky. Motorcycle parking bays exist in the area, particularly around the Domain, and are often cheaper than cars, but they fill quickly on weekdays. Sundays and early mornings are far easier.
Sydney has no shortage of fuel stations, though the city centre itself has few, so fill up in the inner suburbs before you come in. For coffee and lunch, the laneways around Martin Place and the Rocks hold a good supply of cafés and pubs, and the old Queen Victoria Building is nearby.
Walk down to Circular Quay when you are done and watch the ferries cross the harbour. It is the best free show in the city.