Housed in a curvy building reminiscent of a scaled-down Opera House, the Australian National Maritime Museum (sea.museum) – ANMM or Mu-sea-um for short – isn't constrained by what’s beneath its sail-like roofline. Many of the displays are docked outside in the form of tall ships, three naval vessels and other classic craft. The "See It All Ticket" (adult/child $35/25) allows access to all galleries and the bigger vessels, including the replica of James Cook's HMB Endeavour, the naval destroyer HMAS Vampire and the submarine HMAS Onslow.
Exhibitions range from Indigenous seafaring to surf culture, and from immigration to ocean science. There's plenty to fill half a day here, or you can bump it out further by booking a cruise on one of the Sydney Heritage Fleet. The most romantic craft is the James Craig, a three-masted iron barque built in England in 1874, which heads out past the Heads a couple of times a month (from $180; minimum age 12).
There's plenty to do for kids, especially at weekends and in summer, when major exhibitions focus on young visitors.
Other parts of the museum include a free exhibition on wooden boats in the next building north and, opposite Pyrmont Bay ferry stop, the Welcome Wall, a commemoration of migration to Australia that seems particularly relevant in the current political climate.
Sea-kayaking tours with Sydney Harbour Kayaks (sydneyharbourkayaks.com.au; adult/child $89/69) depart out front.