Might be a bit late but the closest would probably be Hennops or Phaladingwe. There are a few about an hour and a half out - Kranskloof, Eagles Cove, Rustig, Shelter Rock, Kgaswane Mountain Reserve and Mountain Sanctuary Park. Otherwise there are plenty of kloofs, waterfalls and other spots in the Magaliesburg if you get permits from either the Jo’burg or Magalies sections of the MCSA or Johannesburg Hiking Club (try Tonquani Kloof, Castle Gorge or the Dome Pools).
For overnights/multiday try Rustig or Kgaswane Mountain Reserve and a bit further out there’s Elangeni, Rhenosterpoort, Kaapschehoop, or the Num-Num trail. Further out and you’re hitting places like Magoebaskloof, Sabie, Goldengate and the Drakensberg/Lesotho. All depends how far you want to go.