One of the spots I visited in Sydney is the Powerhouse Museum. I specifically chose this coz of their exhibition on The Beatles' visit in Australia in June 1964. I was definitely engrossed with the memorabilia displayed, from Lennon's suit during the concert, to the original communication letters for the said event, and this one was my favorite:
I also kept coming back at the jukebox section so I could choose to play my favorite Beatles song while exploring that section. There were exhibits where you get to listen to their radio interviews in Sydney, as well as watch several video clips of their arrival. I should have come earlier; I spent several hours in that section alone, which left me few hours for the other floors of the museum.