Hi Julie -

I can't help with your specific questions, but there's a lot of info here:

http://www.penguin.net.nz/viewing/yellow.html

The Yellow Eyed Penguins are beautiful, amazing, and so rare. I can totally understand why you would want to try and see them even though you have so little time here in Dunedin.

You will be arriving a bit late, perhaps too late to see the penguins. In winter, the Yellow Eyed Penguins start coming onto the beach at 3 p.m. If all goes as planned, you might get out of the airport at 3:40 or 3:45 p.m. Then, if you know exactly where you are going, you can get to the tip of the Otago Peninsula in 70 to 80 minutes (the Dunedin airport is about a half hour out of town). You won't want to drive too fast on Portabello Road (on the Otago Peninsula). Careless drivers sometimes end up in the harbor.

I would recommend you contact these tour operators to see how late they take folks out to see the penguins. They are both based on the peninsula.
http://www.penguinplace.co.nz/penguin-tour/
http://www.natureswonders.co.nz/tours.php

Penguin Place is a working farm that has established a Yellow-Eyed Penguin Reserve on part of their farm. They have spent more than 20 years restoring the habitat for Yellow Eyed Penguins, and have set up a "hospital" to treat malnourished, sick, or injured penguins (not just Yellow Eyed Penguins) found on the beaches of Otago. They also offer lodging, so maybe if you stay there, you can get up early and see the penguins go out at dawn--but that is just my guess, so contact them to find out.

You might be able to see the Little Blue Penguins come in at Pilot's Beach, also at the tip of the Otago Peninsula. The Little Blues come in after dark. Even if you don't see them, you will hear them.

You might see Yellow Eyed Penguins at Sand Fly Bay, if you are lucky. Sand Fly Bay is on the peninsula, but not very far out, so easier to get to. To get to the beach, you have to climb down the sand dunes. The Yellow-Eyed Penguin population at Sand Fly Bay has been declining (I shudder to think what will happen if and when they start oil explorations off Dunedin, as has been proposed). No, you don't have to worry about sand flies at Sand Fly Bay, just flying sand because it is so windy.

When I wrote the Little Blue Penguins come in after dark, I meant twilight, when the last of the day's light is on the horizon. But you can also see them swimming in the water during the day (again, if you are lucky).

We went for a walk to Sand Fly Bay yesterday. Got there at 3:10 p.m. One Yellow Eyed Penguin had already partly climbed the hillside (meaning he probably swan onto the beach at about 2:50 p.m. or so). Another Yellow Eyed Penguin was swimming in the water. I think he wanted to come in, but was frightened by some people standing on the beach. Folks are supposed to keep their distance from the wildlife here and are supposed to stay away from the far ends of the beach (where the penguins swim onto the beach), but rarely do.

We were standing on the sand dunes above the beach (on the Sandymount Trail) watching the wildlife. There were about two dozen NZ Hooker's Sea Lions in addition to the penguins--some of them were enormous.

I was thinking, after checking into your hotel/motel in Dunedin, you might just try driving over to Sand Fly Bay and walking down the sand dunes to the beach. If you get lucky and see wildlife, well, then, great, if not, no loss, as you will at least see this beautiful spot. It does get cold and windy here, so dress warmly.
http://en.wikipedia.org/wiki/Sandfly_Bay
http://www.doc.govt.nz/parks-and-recreation/places-to-visit/otago/coastal-otago/sandfly-bay/

I would suggest checking into your hotel/motel to offload your belongings before heading off to Sand Fly Bay. You wouldn't want your car broken into (not that this often happens, but it can happen).

Thankyou so much for all of that fabulous information. Since planning this trip, and talking to New Zealanders in New Zealand, I have been totally overwhelmed by how helpful and lovely everyone is. It's going to make it hard to continue the traditional Aussie/Kiwi bagging habit of many years!!