Edinburgh Zoo’s penguins are famous, but the current version needs careful wording.
Penguins Rock remains the main place to see gentoo penguins, king penguins, and northern rockhopper penguins. The famous Penguin Parade tradition returned in recent years as Wee Waddle; the official page currently states that the activity is postponed for the foreseeable future because of increased avian-influenza risk in the UK.
So this page does not write the parade as a guaranteed itinerary.

What to see
Edinburgh works because the species characters are distinct. King penguins are tall and steady, like columns in the frame; gentoo penguins are quick, with clear white eye patches; rockhoppers are small but visually forceful.
The Wee Waddle concept is still worth knowing. It lets penguins voluntarily leave the enclosure and approach visitors under keeper guidance and safe distance. Its current pause is a reminder that a popular activity still has to yield to animal health risk.
For another UK penguin route, compare it with London Zoo Penguin Beach. London is Humboldt penguins; Edinburgh is a cold-water group.

How to plan it
If you are coming specifically for Wee Waddle, check the official page before leaving. During the pause, Penguins Rock is still viewable, but do not expect penguins to walk out.
Edinburgh Zoo sits on a hill, and slopes take energy. Put the penguin area in the middle of the route, not as a final rush.
If someone in the group likes history, the story of Sir Nils Olav, the knighted king penguin, is worth reading. But the main line should still return to the group and its care.

Penchan Says
The most important thing in the Edinburgh page is not to romanticize the parade.
The important thing is to admit that it can stop. When avian-influenza risk rises, a beloved route has to step aside. That is the reality of animal care in a zoo.
References
FAQ
Which penguins are at Edinburgh Zoo Penguins Rock?
The page lists gentoo, king, and northern rockhopper penguins, with differences in size, speed, and crest.
Can you count on seeing Penguin Parade or Wee Waddle now?
No. The official page currently says the activity is postponed for the foreseeable future because of increased avian-influenza risk in the UK.
What should you know before visiting the penguin area?
Edinburgh Zoo sits on a hill, so slopes take energy; place the penguin area in the middle of the route rather than as a final rush.