Overall this area is super well conected. If you don't want to take the tube you have many different buses that will take you to the main London attractions.
10 min walk to Clapham Common Station
15 min walk to Clapham Junction (biggest train station)
30 min to London centre (Trafalgar Sq, Oxford Street, Picadilly, Hyde Park, Marble Arch...)
30 min to main London shopping areas