So to be specific, I am actually reviewing the cafe/bar in front of Southbank Centre, and have not in fact attended any performances or anything like that there (well, unless you count the massed preenings on the big deck a performance..). All I can say is that on the right day, this large patio overlooking the Thames and across towards the lovely Art Deco buildings along the Strand is a great place to meet up with some pals and have a few drinks in the sun. The area fills up on hot days, and it can be a bit of a pain to get to the front of the scrum at the bar (which is out of sight wrapped around the back inside the Centre), but you can always just settle for a couple bottles of San Miguel or Peroni from the take-away counter in the front which moves much more swiftly.
A nice walk from Southbank brings you along the river and a number of other promising watering holes, including the BFI bar which can be quite nice on warm summer days as well. There are a number of (mostly chain) eateries in the area to help guard you against getting too pissed, but certainly this is worth a stop in the afternoon for a pint or two. Plus, you can walk without too much trouble to Borough Market to continue the evening and grab some fresh food for the night.