From Simon’s Town, Cape Point and Cape of Good Hope is a nice one day biking ride! You need a special bicycle permit to get into the Table Mountain National Park around the Cape Point area instead of the ‘normal’ conservation fee that apply for hikers. They should promote better the bike, when 99% of the people come by car or bus and you read a huge increase in carbon dioxide in Cape Point!
Cape Point is on the top of the mountain in the East and Cape of Good Hope is more a small hike from the parking slot on the West side and on sea level. Both are connected with a hiking trail, which is doable for a good part on mountain bike (even if the bike are probably not supposed to take it). With a good mtb, going up on the main road to Cape Point and then downhill on the trail is probably the best.
Without that information, I do the other way around where I have partially to carry my bike, but better than going all the way around. In Cape Point, the hiking trail down after the old lighthouse ends quite quickly. Getting a little further down to the newer lighthouse (100y old instead of 200y old!) offers much better views on the big wave in the Cape where you can see the seal fighting with them!
The National Park around the Cape Point hosts quite some wild life: seals, cormorants, Bontehok, local variety of goats, etc., and the famous baboons monkeys that eventually jump on the cars!