Probably a day tour ask at your hotel they will be able to organise one for you.
Car rental or bus tour. I'm not aware of other options (but I'm also not a local).
I know you've said that you don't want to rent a car, but I just wanted to advise you that it was cheaper to rent when we went in Feb. It may be worth looking into that.
When I spoke with the tourist advisor at our hotel this is what he advised, because although the tours are more convenient for people they are also more time consuming (some tend to drive around for an hour or so to pick locations) and you have to stick to a strict time schedule and itinerary. One or two of them also include things you may not be interested in doing like going to the crap chocolate factory, going to the neighbours set or doing a nature walk.
When we got to penguin parade we spent most of the evening there, when we came out we did actually notice (because of the tourist advisor comments) that the coaches had all left, this was about 10:00, so they couldn't of spent much time there viewing the penguins.
I'd really advise you to do some research into both options and book what you feel is more suitable.
FYI with regards to other transport, you can't get a train there and if I remember correctly it was something like 3 buses and then a long walk and you certainly couldn't get a taxi there (maybe after the 3 buses) - also the one bus service was an early finish that wouldn't of worked for us!
Public transport isn't an option unless you want to stay on the island overnight & your accommodation has a shuttle to the Penguin Parade.
If there's more than one of you, renting a car will give you more flexibility as well as probably being more economical. It's an easy drive down to the island.
If it's just you & all you want to see is the penguin parade, then the Little Penguin Bus is probably your best option. They have good reviews here on TA & leave later in the day.
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