If you're looking to learn about Sydney's social and architectural history, this is a good place to visit. Built in 1816, without permission from London, to house 600 male convicts. These convicts then were used as labour for several public works projects. It was the philosphy of Governor Macquarie to use convicts to build grand public buildings such as this one and many others in this part of Sydney. This one and many others were designed by convict-architect Francis Greenway.
The museum has a lot of information about both of these men as well as the historical context of early Sydney. Quite interesting, even if or maybe especially if you're non-Australian.
The building is a grand building with an outer wall, courtyard, and surrounding buildings. Don't just spend your time in the main building itself. Wander the courtyard and visit the old courtrooms that make up the outer rim of the compund.
There are exhibits about the excavation of the barracks back in the late 70's/early 80's. You'll also see exhibits about the tiem the barracks took in single immigrant women. Another interesting piece of the area's history.
The exhibits themselves are informative and interesting but not flashy or interactive. With a few exceptions. The ground floor has a well put together exhibit showing the different layers of the foundation and other interesting things about the building. And up on the fourth floor you can swing in the prisoners' rough hammocks. There's also computer terminals which allow you to search for selected information on the convicts themeselves.
For only $6.50 it's worth spending a few hours here. You'll realy enjoy it if you enjoy history and learning. If you don't really care about doing this kind of stuff on your vacation, well you may be just as happy walking by and admiring the building or missing it all together.