The Barbican is worth visiting for it's brutalist architecture alone. The concert programming is really diverse; it's home to the BBC Syphony Orchestra, but you'll also find bands like the Dirty Projectors and the National amongst the classical and contemporary composer line up. Plenty of art, dance and theatre too, however, the Conservatory is the real gem that's not to be missed.
The Barbican Estate is a residential estate that was built during the 1960s and the 1980s. An icon of Brutalist Architecture the Barbican Estate is an unique and complex real life experiment; a city within a city. The main focal point of the estate is the lake and its neighbouring terrace. High above and behind the terrace is the Barbican Centre, the largest performing arts centre in Europe. I really rate their visual culture exhibitions (for instance, Jean-Michel Basquiat and the Bauhaus) and live concerts (Nils Frahm and Ryoji Ikeda). Love it!
These giant spectral cylinders are great at different times of the day but my favourite time is around dusk when the buildings in the city start to light up. The Gherkin and the new Shard building are framed in the lowest ring then the shifting colours of the sky are almost split in the following ellipses.