The Barbican is both a building and an argument, that Brutalism can be beautiful, that cities can be self-contained worlds. The arts centre inside delivers everything: the best film programme in London, major international exhibitions, the LSO in residence, and a tropical conservatory that's free on Sundays.
Wander before or after, the elevated walkways, lakes, and residential towers reward exploration. The food and drink inside is better than you'd expect.