As a born, bred, and resident South Londoner I feel compelled to beg to differ. For example I'm yet to discover something in North London as wonderful as the Crystal Palace dinosaurs: https://en.wikipedia.org/wiki/Crystal_Palace_Dinosaurs
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.
But yes, it is a lovely city (though because of its size it's hard to "go around" if you don't know what you're looking for exactly)