Well known walks up to the top of Table Mountain which require a good level of fitness include Skeleton Gorge, Nursery Ravine and Platteklip Gorge.
Something to note is, if you come across signage that says, difficult and dangerous route. Take it seriously. These are not merely cautionary signs, but reflect the incredible danger that the mountain can and does pose. Each year, numerous tourists are rescued off the mountain, having strayed from the paths and gotten lost, been unprepared for a sudden change in weather or suffering from heat exhaustion. The mountain is a wilderness area. Always wear the correct shoes, take enough water, be prepared for a sudden change in the weather and take a mobile phone. Tell somebody where you are going and never walk alone.
For slackpacking enthusiasts (you carry a daypack and your heavy pack and food gets taken to your overnight stop) the Hoerikwaggo trail is a must do. The total trail is a 5 day walk from Cape Point to the cable station at the top of Table Mountain. However it is possible to do shorter sections of the trail. A fully catered option, taking you from the historic wash houses at the base of Table Mountain, up to the restored overseers cottages at the top where you overnight, then along the north west edges of the mountain and down, ending at Kirstenbosch Botanical, is available and is highly recommended.
Tel: +27 (0)21 683 7826