The Hayward Gallery in Southbank center has held my favourite exhibitions in London and each time they are extremely well curated. Definitely a place to visit !
Good, progressive, solid, forward-thinking place. And run by the warmest, most intelligent and inspiring people to be around. Always a humble, fulfilled visit. And whilst in the area, best to visit next door to Hannah Barry's gallery for more wonderful work.
A place that really grows on you, with each visit the Barbican reveals more of itself to you and your bond is tightened. The Barbican Kitchen is great for coffee or lunch, summer hangouts by the ponds, cinema in winter, the amazing Barbican Hall for live music, and don't miss the conservatory.
I love swimming and I love being outside. London is great if your into both these things. I swim at London Fields Lido which is heated all year round. Its best in the winter when the steam rises from the water and if your lucky its snowing a little on your head. If your brave you can also go for the unheated option of the Serpentine or Hampstead Ponds.