Kleinmond is awesome. No access issues currently.
Even closer to Strand is Surfside (just outside of Gordon's Bay), which is being rebolted by the locals. The routes there are quite hard (I think 22/23+)
There are no sport routes on Table Mountain, but you might want to check out the Silvermine crags or The Mine if you're in the Cape Town area.
Another brilliant option is Hellfire in Du Toits Kloof, and even Paarl Rock.
All of these are within 45min-1h from Strand.
Check out the wiki on this site for more details.
Hope this helps.