Things have come to a pretty pass when the old is a breath of fresh air and the new just old hat, but the Frieze Masters art fair in Regent's Park, which closes this weekend, is just that. New sister to Frieze London, which features art since 2000, Frieze Masters is about the best of what came before. And boy is that good.

William Klein’s exhibition opens with Broadway by Light (1958), a celluloid elegy to advertising made in the days before neon. Myriad bulbs flash the names of brands like Coca Cola, Camel, Budweiser and Pepsi across New York’s night sky. Silhouetted against vast hoardings, men perch on ladders to hang letters outside Broadway theatres or screw in brightly coloured bulbs that create gaudy, syncopated patterns which, when reflected in rainwater puddles, ripple and shimmer with the subtlety of abstract paintings.

Half-way through Death in Venice, Thomas Mann's tragic hero, Aschenbach, settles down on a beach to gaze out to the sea to "take shelter from the demanding diversity of phenomena in the bosom of boundless simplicity". Aschenbach is suddenly returned to earthly complications when the horizon is intersected by the boy he desires. The passage is evoked on entering Pace’s new and enormous Chipperfield-renovated gallery as suited attendants walk among Rothko's hard-edged late paintings and Sugimoto's seascape photographs.

There are two films in the Turner Prize exhibition and taken together and watched end-to-end they last just under three hours. That sounds gruelling for an art exhibition, but they’re from the strongest two candidates on this year’s shortlist. And since neither is one of those poorly filmed and edited pieces that are best viewed as moving wallpaper as you drift in and out of the gallery, both are worth devoting time to.

On the evidence of this Serpentine exhibition of huge sculptures, small sculptures, photographs, drawings, watercolours and prints, the German artist Thomas Schütte is obsessed, but obsessed, with faces. It is billed as the first show to focus entirely on his portraiture, of himself, his friends, and from the imagination. And the focus helps the visitor to grasp how playfully serious – or seriously playful – the artist is.  

Alonso Berruguete, Vicente Carducho, Juan Antonio Conchillos y Falco and Pedro Machuca are hardly familiar names in the Anglophone art world, but their drawings are on view in a revelatory exhibition. The British Museum is showing nearly all its Spanish drawings and a fine, succinct collection of prints, in an anthology called From the Renaissance to Goya. 

A Dancing Satyr leaps into the air, his head thrown back in ecstasy. His alabaster eyes appear like two pinpoints of illumination in the dimly lit gallery. The bronze figure, which is the first work you encounter in an exhibition spanning 5,000 years of bronze sculpture, is believed to be the work of the famous Greek sculptor Praxiteles, who was active in the second half of the fourth century BC.

On the 35th anniversary of the year punk met the mainstream, it’s to be expected that retrospection and nostalgia are in the air. Television has had a go, albums are being reissued and old soldiers are telling their stories. By its very nature an anniversary suggests that things were cut and dried, that 1977 was a beginning or a marker in the sand.

The vividly dramatic story of Isabella, from a poem by Keats (in turn from Boccacio’s Decameron,) crying over her lover Lorenzo, who, base born, was murdered by her brothers, was much admired by the Victorians. The tale is not for the squeamish: the widowed mistress resolutely dug up the corpse and detached the head, which she then buried in a pot of basil.

There are two exhibitions of Cy Twombly's work at Gagosian Gallery right now. One is fine and will detain you for a few minutes. The other is exactly the revelation we want to refresh and enhance Twombly for his afterlife.