It's deceiving for tourists to think they are experiencing south London if their only experience of it is the South Bank but, to be fair, the great North / South divide means that this is the reality for even native Londoners.
The Tate Modern, an old power station renovated to house the Tate's contemporary art collection, stands guard at the east end of the south bank, with the London Aquarium and the London Eye marking off the west end. The area of riverbank in between houses the British Film Institute, Royal Festival Hall, and the National Theatre, amongst other institutions and venues. Gabriel's Wharf, en route to the Tate Modern, offers up a selection of restaurants for the hungry tourist though, if you can stave off the hunger pangs, then wait until you hit Borough Market, a covered food market by London Bridge station which offers up fresh produce, meats, cheeses, and various tipples. Head to Kappacasein (the queue is worth it) for some hot raclette atop baby new potatoes garnished with small pickled gherkins and you'll see why Borough Market remains a true foodies heaven.