Royal Festival Hall is the most graceful building on the South Bank: a 1951 Festival of Britain concert hall that still feels open, democratic, and unusually easy to enter. The main auditorium is home territory for major orchestras, dance, talks, and festivals, but you do not need a ticket to enjoy the place. Its foyers are open daily, with terraces, river views, cafes, and a steady hum of Londoners using the building as a meeting point.
Architecturally, it matters more than its restrained exterior first suggests. Royal Festival Hall was the first postwar British building to receive Grade I listing, and its clean modernist lines are a useful counterpoint to the heavier brutalism around the rest of the Southbank Centre. Go for a concert if the programme suits you; otherwise, drop in while walking between Waterloo Bridge and the London Eye, especially on a wet day when the free indoor public space is a gift.