if you’re staying near fishoek you should explore silvermine reserve and the elephant’s eye cave. see alison westwood’s blog for a detailed description here (also clickaround on her page - lots of cool options):
Not to be a naysayer, but there are a few hotspots on our beautiful Table Mountain, where it is strongly discouraged to hike alone. So if you are on your ace, I would advise Constantia Nek. You can hike up to the dams and there are always lots of ‘traffic’. Platteklip is also a popular route. It is on the front face of TM. You travel on Tafelberg Road about 3kms from the Lower Cable Station towards Devils Peak. Hiking up “Platties” gives you a lekker workout, AND you are rewarded with some spectacular views up top. Then there is the Cape Point Nature Reserve, a bit pricey to enter if you dont have a green card, but well worth the visit.
You can also check the web for any hikes organised by clubs like Meridian, although I believe there is a small fee for non members joining on an adhoc basis.