It's pretty well known now that Sophia Coppola is the daughter of Francis Coppola (or, when it suits him, Francis Ford Coppola), and if you need to ask who he is then what the hell are you doing on this site? Sophia started out as an actress in her father's films, but her performances in The Godfather, Part III and Coppola's section of New York Stories had critics holding their hands to their heads in disbelief. What was daddy thinking? The acting career thus clanged to a halt and, a few years down the line, Sophia turned to directing. This news initially also prompted groans - Dad's a director, so I'll be one too - but all that was firmly silenced when Sophia delivered her first film, the intelligent, insightful and compelling The Virgin Suicides. Far from being in her father's shadow, Sophia had in just one film carved her own directorial style, and for my money had made a film that was superior to anything her once great father had directed in some time. All eyes were thus on the second film - would it confirm her talent, or mark The Virgin Suicides as an inspired one-off? Well, ladies and gentlemen, the news is generally good....

Bob Harris is a successful action movie star who has reached middle age and has agreed to do a whisky commercial on Japan for the princely sum of two million dollars. On arriving in Tokyo he immediately feels disconnected from both his homeland and those around him, a stranger in a strange land, unable to sleep or find any way to amicably pass the time. Staying at the same hotel is the younger and equally lonely Charlotte, whose photographer husband barely stands still long enough between assignments and client meetings to hold a complete conversation with her. Inevitably the two meet, and a friendship develops that shows signs of leading to something more.

Lost in Translation arrives in the UK on the back of some phenomenally good reviews, and it's easy to see why. Although executive co-produced by Sophia's father, this is an independent work that does what all good indie films should by refusing to push all of the expected Hollywood storytelling buttons, resulting in a beguiling, bittersweet tale of friendship and love that often feels more European than American in its approach and handling. Much of the developing relationship at the film's centre plays as you'd expect, but just as much does not, and certainly towards the end refuses to bow to preview audience-driven Hollywood predictability, which I just can't go into without ruining this element of the film for newcomers. There is a subtlety at work here almost unheard of in American mainstream cinema, a gentleness of approach and pacing that had me intrigued from the opening frames.

What really sells it are the performances of the two leads. Bill Murray is close to his Rushmore best as Harris - tired, confused by his location and its people, wearily dealing with a wife and family at the end of a mobile phone with a colourful ringtone and sometimes iffy reception. He is a delight to watch throughout, communicating so much with so little, the essence of great screen acting. But he is matched almost note for note by Ghost World's Scarlett Johansson as Charlotte, whose disappointment that her life is just not turning out the way she hoped is constantly on the verge of breaking through, but always just kept in check. With her there is a sense of a free spirit whose wings have been, if not clipped, then damaged. Her friendship with the older Harris is at first a pleasing distraction, but later awakens in her something her marriage seems to have repressed. Harris, on the other hand, appears to going through a classic mid-life crisis ("Did you buy a Porsche yet?" Charlotte asks him on recognising this - "You know I was thinking about buying a Porsche" he replies) - certainly his life seems to have lost its focus, and though he is not really looking for something to connect to, he certainly recognises it when it appears. What he doesn't know is what to do about it, and that's one of the strengths of Coppola's handling of their developing relationship - despite his wealth and fame, Harris still emerges as an Everyman, with all the awkwardness and uncertainty that comes with venturing into the unknown, with potentially risking everything you have come to know as safe for what may or may not be nothing more than a passing fancy. This is most effectively realised in an overhead shot in which the two of them lie next to each other on a double bed and just talk - although there is a definite sense of what could happen, their collective caution is always visible their in their body language and the way they speak. It is a scene that I, for one, recognised instantly as real. Throughout the film, that was the thing that struck me the most - that I believed this relationship, every moment of it, every nuance. And that's a hell of an achievement.

Coppola's handling of her actors is matched by her technique, an unflashy mixture of handheld and formally composed shots and a resolutely unhurried editing style give the film a lovely, easy pace. Her choice of music for the soundtrack, which ranges from The Chemical Brothers to Death in Vegas to The Jesus and Mary Chain's Just Like Honey (a great song whose lyrics are perhaps a little too literal in their description of on-screen action but which nonetheless feels so right) could make it one of the must-have soundtrack albums of the year. It should be noted, though, that despite the Tokyo setting these are all western tunes, not Japanese, emphasising the fact that the action is viewed from the viewpoint of an outsider.

So is everything in the film this good? Well, no. Considering the gently realistic nature of the central relationship, other elements and characters seem less well handled. The is a shortcut crudeness to the portrayal of the couple's other halves: Harris's wife, clearly more interested in her house than in their marriage, sends him faxes of shelving unit plans and Fed Ex parcels of carpet samples for him to choose from, while Charlotte would have to be completely daft not to notice husband John's woman-chasing, most noticeable in his exaggerated awkwardness when she insists on accompanying him for a drink with Kelly, a cartoonishly ditsy Los Angeles actress from John's past whom he is clearly keen to have another crack at. Which is all fair enough - the film isn't about them, and the information is communicated quickly, but if the main characters are painted in oils with the finest of strokes, the supporting players are all sribbled in poster paint with a wallpaper brush, and the two make decidedly uneasy bedfellows.

More clumsily handled is the culture clash between Harris and his Japanese hosts. It is somewhat ironic that, having won a Golden Globe for Best Musical or Comedy, it's the comic elements that, for me at least, just don't work, and where the film's indie sensibilities seem to desert it. The Japanese, with their unique unification of modern and traditional and their very different approach to both work and play, have often been the target of "They're funny because they're different" comedy, both here and (especially) in the US, usually through the use of crude and even offensive stereotyping. Coppola is gentler in her approach, but still relies on a variety of somewhat tired ciphers to portray Harris's outsider status, with the result that the Japanese are sometimes presented not so much how they are, more how Mr. Average American expects them to be.

The culture clash is very real and happens in every country, but it is surely the responsibility of the outside party to adapt to the ways of the society they have chosen to visit. In the otherwise formulaic 1992 Tom Selleck vehicle Mr. Baseball, an early scene has his character causing great offence through his ignorance of Japanese bathing traditions, but the sequence manages to avoid the expected traps precisely because that very ignorance is shown to be the cause of the problem. Indeed, in Japan to this day you can find signs requesting the western visitors not to take soap and shampoo into communal bathing areas, and respectfully asking those ignorant of Japanese custom to remove their shoes before entering sacred temples, something I watched an American backpacker completely ignore, prompting a flurry of protests from the priests, with whom he attempted to communicate by speaking English very loudly and very slowly.

Through its effective identification with Harris from the opening scene, Lost in Translation can't help but suggest that it's the Japanese, with their supposed inability to speak English as we do ("You know Lat Pack?" asks a photographer, which Harris translates patiently as "The Rat Pack") and their strange customs and working methods, that are mainly to blame for Harris's sense of isolation. This is at its clunkiest in a sequence in which a somewhat ludicrous prostitute is sent to Harris's room and orders him to "Lip my stockings, please?", a scene that dissolves into farce and just feels hopelessly out of place in light of the subtlety on display elsewhere. Similarly, Harris falls victim to an electronic, pigeon-English-speaking exercise machine with a will of its own (actually cross trainers are powered completely by the efforts of the operator and do not have motors, but there you are), observes with mild bewilderment an exercise class being held in a swimming pool (they hold these daily at my local health centre), gets harassed by the commercial director's inability to speak English (you'd think that for a two million dollar fee Harris could have maybe learnt a little Japanese) and, as have several Americans in movies before (David Naughton in An American Werewolf in London comes immediately to mind), silently passes judgment on a nation's culture by flicking despondently through the TV channels, all of which, of course, are showing rubbish. Not like US or UK TV, then. Additionally, Harris is at his most cheerfully energetic when out with Charlotte and making wisecracks at the expense of locals who cannot understand what he is saying. Which is, of course, just how some Westerners do behave when abroad, but the effect was immediate on me - I started to get irritated by someone I had really grown to like. Much of this is relevant to the story and character development, of course, but would have worked better had it not relied so much on stereotype and cheap attempts to get laughs.

Balancing this to some degree is Harris's slow acceptance of aspects of the Japanese culture, initially elements with which he is already familiar - going to parties and clubs, dancing, chatting in bars - but a turning point is reached during a jovial karaoke session that wonderfully captures the essence of a drunken night out in a karaoke club in a Japanese city - I know, I've done it, and can testify to the almost documentary nature of this scene, an element emphasised by the hand-held camerawork and boisterously off-key singing. It also functions as a believable catalyst for Harris's shift of opinion on his surroundings - later he sits in a spa bath and talks to his wife on the phone about eating more healthily, "like the Japanese," which prompts her to suggest that he stay there and eat all the Japanese food he likes. At that point, despite his earlier desire to get the hell out, you believe he just might.

Although some of the moans might sound like I'm making a big issue out of seemingly little, at least when when so much of the rest is works so well, these moments are like unsightly cracks in a finely glazed vase, temporarily disconnecting me from an engrossing narrative and reminding me very soundly that I am watching a movie, and, in all that is negative in that term, an American movie. Even when American film-makers take an honest cinematic look at themselves and their way of life, they still too often seem unable to apply the same perception and depth to other cultures, often seeing them in somewhat one-dimensional terms, something to be observed rather than understood.

My reservations remain, but in many other ways this is still an impressive work, and I would encourage anyone with an ounce of sensitivity to hunt it out. It certainly left me with a smile on my face, and if the simplistic nature of some aspects and characters seemed a little too typical of American mainstream movies, the central relationship most definitely was not, and it's this aspect that fills me with hope - for Sophia Coppola's future projects, the the triumph of subtlety over excess, and for American independent cinema in general.