The New York theatre is so consistently awash in "star is born" moments when one or another British actor crosses the Atlantic to copious praise that it's lovely for a change to be able to reverse the kudos. And as Phil Connors, the jaded weatherman for whom February 2 threatens to become a personal Waterloo, Broadway veteran Andy Karl in his London stage debut sends the stage musical adaptation of Groundhog Day soaring.

Southwark's golden triangle – the Menier, the Playhouse and the Union – has given us so many "lost" musicals which only a decade or so ago would have been lucky to get in-concert airings.

Alix in Wundergarten ★★★★

Think Alan Ayckbourn on acid: a commonplace (well, almost) set-up, exaggerated further and further beyond what we’d ever anticipate.

If you like the feeling of leaving a show, surrounded by the gently glowing faces of happy fellow audience members, then this is one for you. It’s a musical evening full of joyful singing – mixing classics by Mendelssohn and Bartok with a best-of chunk of the back catalogue from the Electric Light Orchestra’s Jeff Lynne – that transports you to a different world.

Billie Piper vaults to the top rank of British theatre actresses with Yerma, Australian writer-director Simon Stone's rabidly free rewrite of Lorca's 1934 play that posits its young star as the sort of take-no-prisoners talent whose gifts come not from drama school but from something gloriously unfettered and astonishingly free.

"Yes, from life," Nikolai Ivanov (Geoffrey Streatfeild) says in passing of a painting midway through the early Chekhov play that bears his name. But the phrase could serve as the abiding achievement of the largely thrilling triptych of plays that has transferred from Chichester to the National under the banner title Young Chekhov.

Think of Holly Golightly, and it’s more than likely that the face you’re picturing is Audrey Hepburn’s. And, while this adaptation by Richard Greenberg of Breakfast at Tiffany's is much closer to Truman Capote’s novella, it doesn’t have an ounce of the appeal of Blake Edwards’ famous film. Directed by antiseptic efficiency in a Leicester Curve production by Nikolai Foster, it’s numbingly dull  – a dreary, inert tale of brittle, dislikeable people, inhabiting a tastefully designed bubble that is rarely pricked by events from the outside world.

How many genders are there? The simplistic answer is two, but if you really think that then it’s time to go to the back of the class. In recent years, the rapid growth in perception of the fluidity of gender identity has meant that although there has been an increase in transgender stories in the news, culture has lagged a bit behind. Now every art form wants its own Danish Girl. Playwright Jon Brittain was inspired to write the hugely enjoyable Rotterdam after a couple of his friends transitioned in the late 2000s.

Anniversaries are lotteries. Sometimes they allow us to see the past with fresh eyes; at other times, they simply accentuate the growing distance between then and now. Because this year marks the centenary of the Easter Rising of 1916, the National has decided to revive Sean O’Casey’s The Plough and the Stars, whose last two acts are set during the ill-fated uprising against British colonial rule.

Watching Cameron Mackintosh’s joyful revision of this Sixties musical, it’s possible to believe for a moment that all the world needs now is love sweet love and a shit-ton of banjos. With a new book by Downton Abbey behemoth Julian Fellowes, new numbers by the pair behind hit musical Mary Poppins, and design that delights at every turn of the multi-revolve, Half A Sixpence seems destined to follow a flush of previous Chichester Festival musicals into the West End. It also puts vintage stars around the previously unknown name of Charlie Stemp.