No matter how many times I visit, seeing the African penguin colony in Simon's Town always makes me smile. The actual park, Boulders, is run by SANParks and features a (free) boardwalk along the edges of the park, where you'll see penguins nesting and living. There is also a paid entrance that will take you on another boardwalk, down to the beach where the penguins congregate for a better view. If you're bringing the kids, this is the way to go.
For the best view, park at or walk to near where I marked on this map. Proceed through the Boulders parking lot towards a tiny, wooden gate. Open it, and you'll find a smaller pathway leading to the area pictured here. This is a public area, albeit very close to some private homes. This turns into a pathway which allows you to get much closer, without any barriers to the waterfront, to observe the penguins in their natural habitat.
Simon's Town is easily accessible by driving, or by train (last stop on the Southern Suburbs line and a short walk through the historical, naval town).