The Immigration Museum uses voices, images and memorabilia to tell the many stories of Australian immigration. It's symbolically housed in the old Customs House and the restored 1876 building alone is worth a visit: the Long Room is a magnificent piece of Italian Renaissance–revival architecture. Keep an eye out for workshops and special events.
After exiting the museum, head across the river via Sandridge Bridge to check out the steel Travellers sculptures, which depict the story of arrival that belongs to many Melburnians. Gayip, the only sculpture to sit on land rather than on the bridge, represents Indigenous Australians from the area.