Maybe an obvious choice, but the Barbican is always good. My favourite space in there is the curve gallery, last time I went was for Cory Arcangel's 'Beat the Champ'. I love the architecture, although not many people do. I think it was voted 'London's ugliest building' in 2003.
Not been in many years, but spent a large part of my childhood watching people row and sail back and forth. It freezes over in winter and in February 1893, Jack Selby drove a coach and four horses across the reservoir.
Need some clean air or just a time-out? Kew Gardens is a short train ride away from the city centre but is provides you with space, greenery and and a small holiday for the lungs. The garden contain tropical glasshouses and interesting architecture, so it is a treat for both body and mind.
You would have seen the Brutalist towers and curves from afar. Upon entering the estate where the cultural centre is, you quickly realise the scale, the beauty and charm of this labyrinthine project. Barbican Centre's programming is top of the league across art, theatre, dance and music, both contemporary and classical, art forms. This place is an architectural and cultural institution boldly redefining the UK's cultural landscape.