Quite a few places to see the fairy penguins in the wild in Oz... Kingscote & Penneshaw on Kangaroo Island, Victor Harbor in SA. They're even spotted occasionally on the Sydney > Manley ferry.

In Tasmania I'd recommend "The Penguin Point" which is on the northern coast between the cities of Ulverstone and Penguin. It's owned by a married couple who discovered after they purchased the property that it was a large rookery. You sit & wait for the wee birds to parade past you and later you can peer into their burrows. Unfortunately June is a couple of months past the breeding season.

Other easy to get to places in Tassie are: Stanley, Bicheno, Burnie, Bruny, and Lillico Beach.