The famous one
Boulders Beach — the colony inside Cape Town's peninsula. Yes, it's touristy; yes, it's worth it. You walk on boardwalks over the breeding area, and the penguins ignore you at arm's length. Go early (before 9am) or late (after 4pm in summer) to avoid the bus crowds; midday is a queue. There's an entry fee; it's a SANParks site.
The quieter one
Stony Point at Betty's Bay, an hour and a half from the city on the Whale Coast — a breeding colony on a rocky point, fewer people, equally close penguins, and a better drive to get there. If you've done Boulders and want space, or you're already on the Whale Coast, this is the one.
The rules
Stay on the boardwalks. The penguins bite, they're wild, and the ones that look cute on the sand are defending nests. Don't feed them, don't touch them, don't chase a selfie. A penguin that's comfortable with you is a penguin that's about to bite you.
Why they're here
African penguins breed only on a handful of southern African coasts, and the population is endangered — these two colonies are among the largest. They're here because of the cold, fish-rich Benguela current. You're visiting a conservation success and a fragile one; act accordingly.