Lion's Head is the sharply pointed peak between Table Mountain and Signal Hill, rising 669 metres above the city. A well-marked spiral path winds around the mountain to the summit, with a section of chain-assisted scrambling near the top. Allow about two and a half hours up and back.
The view from the top is arguably better than from Table Mountain itself, because you can see Table Mountain — the city, the harbour, the entire Atlantic coast, Camps Bay, and the bowl of the city centre all spread out below. Start early to avoid the heat, or join the famous full-moon hikes if your visit coincides with one. The path is steep but accessible to any reasonably fit person.