She raises a small arm with impressive biceps to shake hands.
While other patrons stand in line to order, the waiters, notified in advance of her arrival, bring a menu to her table.
Like many female stars whose biggest parts once seemed behind them, Hunter might have been doomed to the standard mum or spurned wife roles.
But riding the crest of actresses leading television series, she has revitalised her career on the small screen as Grace - a hard-drinking, promiscuous Southern detective monitored by a crusty angel named Earl.
Unlike, say, Kyra Sedgwick in The Closer or Glenn Close in Damages, Hunter's Saving Grace role has veered into new territory as that rarely seen character: an explicitly sexual 40-year-old woman.
In a titillating mix of pleasure and religion, Grace, a driven detective and kindly aunt, often is shown having sex, sometimes with married men, and then debating her behaviour with Earl.
Although some critics charge that her rebel-hero character is tiresome, others also allow that the show pushes boundaries with her coarse language and semi-nude sexuality.
"Grace is a study of human nature first and foremost," Hunter says.
"The allure of Grace is her complexity. She can often entice conflicts, and she surrenders to her desires, what she feels could be the most fun, intoxicating, seductive, tantalising, what could be the most cool. So many people slog through the moments to, say, get to Friday. Grace lives fully."
The Oscar-winning actress was nominated for a Golden Globe for Saving Grace and this year received a star on Hollywood's Walk of Fame.
Hunter says she leaped at the chance to play Grace, because "I wanted to have that conversation with myself, with other characters and with an audience. Movies aren't made about a woman's whole life."
Working in television is, in a way, returning to her roots.
In the 1980s, Hunter appeared in several TV movies and more recently in When Billie Beat Bobby (2001), a TV movie about Billie Jean King; and in American Experience: Abraham and Mary Lincoln - A House Divided (2001) as the voice of Mary Lincoln.
She has won two Emmys for The Positively True Adventures of the Alleged Texas Cheerleader-Murdering Mom (1993) and Roe vs. Wade (1989).
What she doesn't want to have a conversation about herself.
Serious and earnest, Hunter speaks eagerly about the arc of her career, her professional friendships and her intense involvement in the show but turns curt when it comes to her own life - a six-year marriage to cinematographer Janusz Kaminski and her 2-year-old twins fathered by her current partner and actor Gordon MacDonald, who has appeared in Saving Grace.
With a fleeting smile, Hunter says she will neither "confirm or deny" the twins' existence.
She suggests MacDonald not be mentioned at all in the article.
"The world is chock-full of actors and actresses who want to talk about their personal lives. I don't," she says.
"And I really want that respected."
As an actress, Hunter often is described as ferocious, fearless, feisty and focused.
Her movie roles have varied from funny and offbeat (Raising Arizona) to strong and quirky (Broadcast News) and intense and dramatic (The Piano, for which she won the Oscar.)
The youngest of seven children raised on a Georgia farm, she studied at Carnegie Mellon University in Pittsburgh and later moved to New York, making several auspicious connections by sheer chance.
Hunter had a boyfriend, for instance, who wanted her to join him on a visit to Yale to meet his best friend and his girlfriend - who turned out to be Frances McDormand.
"It was a very dramatic night," says Hunter, who is unwilling to tell much more of the story. ("It's a secret.")
"Fran and I bonded over it. We saw each other in the midst of this chaos and we became friends right then."
McDormand eventually moved in with Hunter in New York.
While appearing in Crimes of the Heart, a play by Beth Henley (whom she had met in an elevator), Hunter was spotted by Joel and Ethan Coen, who wanted to cast her in Blood Simple.
Because Hunter was committed to another Henley play, she suggested McDormand, who got the role - and was married to Joel within a year.
The Coens subsequently cast Hunter in Raising Arizona and O Brother, Where Art Thou?
Later, the four friends lived together for four months in Los Angeles.
These days, when she is not shooting Grace in L. A., she says, "We all live in New York. We all hang out."
Saving Grace was created by Oklahoma native Nancy Miller (The Closer), who cast Hunter from a short list of pre-approved actresses. "It was a dream come true," Miller says.
Besides acting, Hunter serves as an executive producer, editing shots, suggesting music, story ideas and even marketing.
She spends weekends in daylong "tone" meetings, and that's in addition to workouts and Pilates training to stay fit.
In the first season, Grace was driving drunk when she hit Leon Cooley, played by Bokeem Woodbine, who turned out to be a death row inmate who also converses with Earl, played by Leon Rippy.
Grace's friend Rhetta Rodriguez, actress Laura San Giacomo, tries to help her figure it all out.
Hunter knows what Grace would and wouldn't say, would and wouldn't wear.
If she isn't sure which finger Grace would use to fire her gun, she'll call the Oklahoma City Police Department, Miller says.
Unlike film characters that actors live with for three or six months, Grace is part of Hunter's life day in and day out, even during hiatus, Hunter says.
Hunter believes firmly in taking time off but that acting is good for her.
She says she feels most herself when acting.
Miller acknowledges the show isn't for everyone, meaning people who might be squeamish about explicit sex or non-sectarian religion.
Her goal was to write about the themes of God and religion, sin and faith through the eyes of a woman who had no faith - Grace.
Earl, the angel, sometimes sounds like an AA sponsor, but he also could be a minister, a Buddhist, a guru or "a person who practices tai chi", Hunter says.
In season 2, currently being shot, viewers can expect more religious push/pull - Grace confronts a priest who molested her as a child.
Grace will have a new partner at work.
And there will be more humour - especially among the cops, Hunter says.
Hunter and MacDonald are occasionally pictured in celebrity magazines with their boys, in New York or at the Hollywood Walk of Fame ceremony.
Living in such a celebrity-driven environment, it must be difficult to . . .
"I don't want to talk about it," she says.
"I don't want to talk about how I nurture or don't nurture my public life. I'm sure you'll spend half the article talking about it now. But, you know, really, it's fine."
• Saving Grace screens on TV3 at 11.10pm on Wednesdays.
