The Lady from the Sea, Almeida, London<br></br>Henry V, NT Olivier, London<br></br>Richard II, Shakespeare's Globe, London<br></br>Sexual Perversity in Chicago, Comedy, London

A young leader, a war. Perfect timing
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The Independent Culture

It's been over two years since the bulldozers rolled up at the Almeida in Islington, and last week's reopening unveiled an impressive rebuild that's chic and subtly industrial, new and in touch with the old (courtesy of Lottery funding). The box-office foyer used to be open to the street, with rusting props stashed behind rotting Portaloos. I was rather fond of the rusty props. However, the foyer now feels both airy and cosy, reconstructed like a lean-to greenhouse, and the angled roof directs your eye to the heart of the place: the 1837 lecture hall-turned-theatre. Inside, the auditorium is, essentially, untouched (improved seats, an updated rig). It's welcome back to the much-loved, curving brick backdrop and the low-slung balcony.

And on stage? Here we find Natasha Richardson in The Lady from the Sea. This sun-dappled yet haunted play – written by the sexagenarian Ibsen in 1888 – marks Michael Attenborough's new artistic directorship. It's also Trevor Nunn's first theatre production since leaving the National, with Richardson as the near-tragic heroine Ellida, who's going quietly mad in the fjord-side home of Dr Wangel, her protective older husband. She feels uncontrollably drawn back to the wilder seas of her youth and to memories of a dangerous ex-lover called the Stranger.

The Stranger is an intriguing figure, coming ashore and calling Ellida to come to him. He seems flesh and blood but also a phantom in her obsessed mind. Unfortunately, Eoin McCarthy's Stranger, though brawny and devoted, appears bland. Richardson's Ellida starts off as a shallow, emotional rill and is, at worst, a drip. She smiles dreamily to the point of seeming brainless, rather than disturbed. Then, with some flashes of true frustration en route, she veers towards melodrama. The thrumming soundtrack, backing eerie moments, is laid on thick, and the denouement where Ellida gets to choose freely, looks like a diagrammatic lesson in early feminism. The quietly naturalistic scenes are a thousand times better. John Bowe is outstanding as the steady but pained Wangel. And Claudie Blakley and Tim McInnerny – playing Wangel's daughter Bolette and her tutor-turned-suitor – are a charmingly comical, nervous and sadly compromised couple. They make the evening memorable.

Meanwhile, Nunn's successor, Nicholas Hytner, stages his first production since taking charge at the National. Tony Blair's political timing has been perfect, ensuring Hytner's modern-dress Henry V seems startlingly up-to-the-minute as regards going to war. The battlefield – a bare, black void – could be anywhere. However, you can't miss the audience's cynical laughter and simultaneous intake of breath when Henry's advisors – in suits and ties – present us with blatantly questionable, satirically convoluted justifications for an invasion. Discontented rumblings amongst the ill-provided squaddies lead to the enemy's mocking cry, "Shall we go send them dinners?" Rogue soldiers are caught with stolen cultural artefacts. Henry's religiously-loaded language has an oddly familiar ring to it too.

Of course, you can spot differences between then and now – not least Henry's archbishop advocating military action. This production does have flat patches, too. At points the verse-speaking fails to pull you in and the battle scenes look stagey. The excessive use of jeeps is especially irritating, and at odds with Penny Downie's Chorus who – narrating like an impassioned media don – keeps urging us to rely on our imagination. Generally, though, Hytner is going for a spartan aesthetic. Though he's famous for flying a helicopter into Miss Saigon, choppers are only heard overhead this time – thank heavens.

Lester is a formidably chilly young ruler in the council chamber, weighing up his elders in silence. However, once on the field, he seems little more than one of the boys, trudging round with a rucksack and making an understated St Crispin's Day speech. This king hardly needs to go incognito to merge with his men. You might think Hytner was naive, taking Shakespeare's egalitarian "band of brothers" speech too literally. But he simultaneously uses video very intelligently, showing the employment of rhetoric in terms of the modern media. Henry's "foreign policy" speeches are repeated as full-blown public broadcasts on a big screen, creating smooth segues and adding an extra level of invasion. The king's grim call-to-arms is watched by the lads in Mistress Quickly's pub – flicking between him and the snooker – and the news is viewed anxiously in the French king's palace (amusingly acquiring subtitles).

In this production, Princess Catherine (Felicité du Jeu), learns English because she's frightened, and Henry's happy ending, as her suitor, is strongly undermined. The defeated French are deeply grieved, only mouthing official welcomes. This play's notorious nationalistic flag-waving is also interestingly qualified by Hytner's multicultural cast.

Making Shakespeare's politicians our contemporaries with microphones and cameras isn't a new idea, but this Henry V is remarkably topical and – playing in the Olivier – it turns Sir Laurence's 1944 film version on its head.

Just along the river at Shakespeare's reconstructed "wooden O", Richard II is less exciting. The Elizabethan outfits are exquisitely tailored but tend to make the play look like a museum piece, as the king's fractious aristocrats duel in clanking armour. This wouldn't be a problem if Tim Carroll's directing was on the ball, but he often lets his actors wander like lost sheep. One might be forgiven for thinking the real tragedy of this Richard II is that the usurper, Liam Brennan's Bolingbroke/ Henry IV, is such a limp bore. Mark Rylance's Richard is mildly disappointing too, though all the potential for a great performance is there. Rylance is wonderful at playing weak men, comically and poignantly. Nevertheless, his quavering voice risks becoming reductive here. He is totally persuasive bringing out a foppish side to Richard – toying with a lace hanky. And the monarch's downfall is certainly seeded in his distracted air which is mixed with arrogance and hysteria – only screaming for order once the situation's out of control. He is also ferociously sarcastic and touching when, deposed, he play-acts a whispering servant beside the empty throne.

What Carroll fails to pinpoint elsewhere is the sharp switches in this royal between floundering and strategic game-playing. Hurrying the king's philosophical and poetic soliloquies, Rylance also misses the dignity that Shakespeare – at least fleetingly – allowed him.

In Rylance's all-male company it's the ones in frocks who usually turn out to be the most forceful, while the two guys in Sexual Perversity in Chicago end up as macho losers, ogling unknown babes in the park. Director Lindsay Posner doesn't try to update David Mamet's 1970's four-hander about the temporarily riven flatmates, Joan and Deborah, the latter's briefly steady sweetheart Danny, and his buddy Bernard – a wannabe-stud full of boasts and misogynistic spleen.

Between Mamet's rapid-fire scenes, Posner plays funky disco hits and flashes up photos of the Windy City in the Seventies. This creates a kind of retro snazziness, orange walls sliding to reveal boxed scenes. However, all this to-do slows down the fast-living action. The cast is droll and well drilled. Minnie Driver's Joan is sexually uptight with a vicious streak, though Matthew Perry's affable Danny is outshone by Kelly Reilly's secretly sharp Deborah and by Hank Azaria's amusingly ghastly Bernard. Entertaining but inconsequential.

'The Lady from the Sea': Almeida, London N1 (020 7359 4404), to 28 June; 'Henry V': NT Olivier, London SE1 (020 7452 3000), in rep to 20 Aug; 'Sexual Perversity in Chicago': Comedy, London SW1 (020 7369 1731), to 2 Aug; 'Richard II': Shakespeare's Globe, London SE1 (020 7401 9919), to 27 Sept