When Eve Hewson was 15, she said she wanted to be an actress.

Her parents weren't thrilled. "They warned me against it," she laughs. "I think they just wanted to know that I was prepared to live in that kind of environment – that cruel, scary, competitive world. Fortunately I was, and here I am!"

The "here" in this case is New York, where Hewson, now 20, is two years into a theatre degree at the prestigious New York University. But "here I am!" could soon also become a refrain of sorts for the young Dubliner as she gears up for the release of her first major film and the publicity her performance will bring. The film is called This Must Be The Place. It's directed by acclaimed Italian filmmaker Paolo Sorrentino and it pitches Hewson into a production which includes some stellar names, prime among them Sean Penn and Frances McDormand. It's hard to imagine a more impressive – or daunting – entree into the world of arthouse cinema. Here I am, indeed: now look at me go.

But first a word about those concerned parents – mum Alison, a businesswoman and fundraiser, and dad Paul, better known as U2 frontman Bono. For them, it's fair to say, a warning against a career in the media spotlight comes with the weight of experience behind it. "Because they're part of that business, they know how crap it can be. It can be awful and really cruel to young women," says Hewson.

She admits, however, that growing up around fame has at least opened her eyes to its potential downsides and, to some extent, armed her against them. "It's true I wasn't just some girl living in a small town wanting to be a movie star. I was more exposed to the pitfalls of that life. I knew it was going to take hard work and that in some ways it was going to be harder work for me because I was going to have to prove myself a lot more. Yet more doors are open to me, so I also had to make sure I knew exactly what I was doing and that I could actually act. That's why I've been training for so many years."

To gain entry to the NYU theatre course, she had to fly to New York and audition. "I was so nervous I puked afterwards," she says. "It wasn't really to prove anything to anybody else, it's just that I wanted to study and get a good education if I could. It's benefited me in my life. I think it was a really smart move."

Smart enough to win her a role in This Must Be The Place, anyway. In it, Hewson plays Mary, a Dublin Goth from a troubled background who befriends a gentle, reclusive and mildly depressive American rock star called Cheyenne. Now in his fifties and a cult curio in his adopted hometown, he quit the business after his lyrics drove a young fan to suicide.

Penn plays Cheyenne as a mixture of Robert Smith and Alice Cooper, though it's hard to imagine either trundling a suitcase on wheels behind them, which is Cheyenne's other style quirk besides backcombed hair and 18-hole Dr Martens. McDormand plays his resolutely normal wife, Jane, and another notable performance comes from former Talking Heads frontman David Byrne who plays himself and, in one memorable scene involving a bizarre musical contraption, "performs" as a disused New York church.

In Dublin, Cheyenne and Mary talk, eat, drink coffee and wander the streets before the film's second act, which takes Cheyenne back to the US, where his Jewish father has died. Part road-movie, part Holocaust survivor's tale, it's shot with the same quiet intensity and precise image-making as previous Sorrentino films such as The Consequences Of Love and Il Divo, which was awarded the 2008 Cannes Jury Prize when Penn was its president. It was Penn's promise to Sorrentino that he would work with the director anywhere and at any time which started the ball rolling on this, the Italian's first English-language film.

Hewson came on board when Sorrentino was looking to cast an Irish actress for the script he had written and to which Penn had already signed up. She turned up for the audition in knee-length biker boots, which the Italian liked and later demanded she wear in the film. The audition itself, however, was not what even her short experience of acting had taught her to expect. "I was kind of confused because I'd worked so hard for the audition and was so stressed out about it and had so many different emotions," she recalls. "Then I walked in there and he didn't even ask me to read. I thought 'Is that a good thing or a bad thing?'."

At the time, she maintains, Sorrentino didn't know her from Adam – the biblical one, not the U2 bassist – so had no idea who her father was. "He didn't seem to be interested in any of that," she says. "He was just interested in making his movie and who was right for the part and thankfully I was. He never said anything to me about it."

Nonetheless, it's notable that he cast her to play opposite an actor pretending to be a fiftysomething rock star when that's exactly what her own father is. Did it feel familiar in any way? "It wasn't familiar at all," she laughs. "That character is completely different to who my dad is, so I didn't really see any similarities at all, other than that Sean might look like my dad a little bit. But not in that wig or in his voice or mannerisms."

In truth, the relationship between Mary and Cheyenne is far from a mirror image of Hewson's own home life, which was as normal an upbringing as you can have when your father sings in the biggest band on the planet and has half a dozen world leaders on his speed-dial.

The second of Bono's four children, Hewson attended fee-paying Dublin day school St Andrews College, but beyond that it was a get up/go to school/come home sort of existence, with only occasional interruptions for drama classes and backstage trips to U2 gigs. "I don't get handed money and I never will," she has said.

So while the singer himself maintains a fancy duplex penthouse apartment in New York's Upper West Side, it's strictly out of bounds to his daughter. Instead, she lives in New York's less salubrious but more bohemian downtown area. If there are rock stars on her block, you probably haven't heard of them yet. "I actually just moved," she says. "We had a mouse infestation. I found a mouse in my bed, which was the most disturbing thing in my life. So I had to move out of there and now I'm in Chelsea. I can still get to class in eight minutes on the subway."

That's not to say there aren't some differences between her and her classmates. Hewson had never met Penn before landing the part of Mary, but the actor knew her father of old. Penn turned 50 during the Dublin part of the shoot so Bono organised a very special – and very Irish – birthday party for him. It involved lunch, a literary walking tour, much Guinness and, in the upstairs room of a pub, a specially-organised gig by The Dubliners. Kris Kristofferson turned up too, and treated Penn to a rendition of Me And Bobby McGee.

At the time, Hewson had other things on her mind besides starry lock-ins in Dublin pubs. Uppermost was how to prepare for a potentially career-making role opposite a double Oscar-winner hailed as one of the greatest actors of his generation. Homework involved watching every film Penn had ever made. "Preparing to shoot scenes with Sean Penn, you can't really take that lightly," she says. "So I was nervous and scared. I was just hoping we could form a good relationship because I wanted to be his friend."

It seems to have worked. "We hung out a lot after shooting and got to know each other," she says, slipping back into a Dublin brogue which sometimes struggles against her American twang. "He's a prankster, too, and really funny. Not many people expect that from him. He's a lot of fun to hang out with."

Penn has moved on to other projects, and to the fundraising work in Haiti which occupies an increasing amount of his time. But there's much excitement in the Hewson household ahead of Friday's release of This Must Be The Place. "It's weird because I'm not at home," says the young actress. "All my friends are texting me and saying 'Your movie's coming out, ha ha' and my mum's saying she's going to go and see it at the weekend. But I'm so glad I'm not there because if I was I'd be so embarrassed. I know all my friends would laugh at me. So I'm kind of dreading it."

Dread or not, the search for parts will continue. Hewson hopes to finish college a term early, in December 2012, and then throw herself full-time into theatre and film. When that happens, the chances are Bono's actress daughter will find a lot more of what she's looking for.

This Must Be The Place is released on Friday

wHAT BETTER FILM ROLE FOR bONO'S DAUGHTER THAN STARRING OPP0SITE SEAN pENN'S FIFTYSOMETHING ROCK STAR? bUT barry didcock discovers THIS WASN'T exactly A CASE OF ART IMITATING LIFE