Also Greenwich Park, Greenwich generally, Brixton and Kew Gardens. Still, none of these extends much past the river.
And the IWM, the Old Vic and the Young Vic, and Elephant and Castle, and Lambeth Palace and Clapham Common, and Blackheath and the Peckhamplex. There's loads going on in South London.
Yeah looking at her Google timeline maps that she posted, when she went to the "south bank" she actually walked around Waterloo station.
A walk along the actual south bank (of the river) I would say should be a must for any tourist in London. Great view of the Thames, no cars, interesting architecture, and plenty of galleries and other cultural highlights. In particular the Tate modern.