A town in desperate need of regeneration commissions David Chipperfield, the architect of the moment, to build an art gallery in the hope of attracting visitors with deep pockets. In case you are suffering an attack of déja vu, this is not an action replay of the opening of Turner Contemporary in Margate a month ago, but Wakefield’s turn to use the same tactics.

Max Bill might be the missing link in modern art. He died only in 1994, yet he studied at the Bauhaus in Dessau in the 1920s, taught by Josef Albers, László Moholy-Nagy, Paul Klee and Kandinsky. It is hard to imagine that someone who was working at full strength less than 20 years ago could have a past that is so strongly entwined with these legendary names – hard to imagine, that is, until one looks at the work displayed in this fine retrospective, which even so manages to encompass only five decades of a nearly seven-decade-long career.

John Cage, the focus of an adventurous three-day mini-festival in Bristol, is possibly one of the most influential figures in 20th-century culture. As much a practical philosopher as a composer of note, he made artists, writers and musicians think about the nature of chance, our place in nature and the role of the subject in the creative process.

At its best, and most preposterous, John Cage's work can be a mind-cleanser. The overwhelmingly silly randomised conjunctions and ontological punning of the great Zen master of the 20th-century avant-garde can coax and trick you into letting go of categories and judgments, scale and expectation, and just letting yourself get swept along with the gloriously complex and profoundly nonsensical multidimensional parlour games. Where some artworks might make you feel like you're on drugs, or

Avant-garde art, by its very nature, always treads a fine line between the sublime and the ridiculous, and between entertainment and alienation. Thankfully this is something understood very well by the joint curators of Friday night's show at the Vortex Jazz Club: Baron Mordant of the Mordant Music record label and Jonny Mugwump of the Exotic Pylon website and radio show. As the names perhaps suggest, these are people versed in the potential deep silliness of what they do, even as they take it very seriously indeed – and their event certainly ranged far and wide between the weird, the wonderful and the out-and-out wrong.

Who could not love Martin Creed? The tweed-encased harumphers of the world adore him, because they can say, “That’s not art,” and, “My cat could do that,” and have an all-round wonderful time. Conceptualists have it easy: what could be more fun than his Turner Prize-winning Work No 227, a light going on and off in a room? And lovers of abstract art love him because his work is just there. “Take it or leave it,” it seems to say. And they love him because, well, because his work is lovable.

Well, we all make mistakes. Or, in my case, we (I mean “I”) sometimes just fail to look. This new, small but perfectly formed exhibition of Bridget Riley’s work in the National Gallery’s Sunley Rooms follows the pattern that the gallery has developed over the years, with a single artist entering into a conversation with the great art of the past. Riley’s conversation is gripping, and one of the things it says (to me) is, “Shame on you for not looking.”

Tonight the company dedicated to the greatest radical of modern dance, Merce Cunningham, opens its farewell tour to London, a valedictory odyssey that will end next year. Last year Cunningham died, aged 90. He had just premiered a work called Nearly Ninety, and this is fittingly the last thing we will see of his company as it blazes one final circuit before closing down in December 2011.