The building where the Hyde Park Barracks is housed is itself one of the museum exhibits. That's not unusual -- many of the great museums of the world are situated in former mansions or palaces, and when I visit houses of historical value that are open to the public I'm usually more interested in the house itself than in whatever dishes and snuffboxes are sitting in the glass cases.
The history of this building -- designed by the great Francis Greenway, himself a convict, built by convict labor to house convicts, before becoming a home for immigrant women and finally government offices -- is like a summary of Australian history in brick and plaster.
What they've done here that's fascinating is to strip away many of the additions made through the years without trying to recreate the original. This stairwell no longer has stairs, only an iron railing to mark what used to be there.