Table Mountain is the defining landmark of Cape Town — visible from almost everywhere in the city, it serves as a constant compass point and one of the most recognisable natural monuments in the world. On cloudy days, Capetonians call the low-hanging cloud the "Tablecloth."
You can reach the summit by cable car or on foot. The cable car rotates on its way up, giving 360-degree views, and takes you to a visitor centre and café at the top. Several hiking trails wind up and over the mountain — most are manageable for fit walkers, but check conditions before you go.
At the top, dassies (rock hyraxes) wander among the visitors — small, round, furry creatures that are, implausibly, the closest living relative of the elephant. On a clear day you can see the Cape of Good Hope to the south, Camps Bay to the west, and the whole of Cape Town spread below. Go on a clear day and bring more memory cards than you think you need.