It's hard not to fall in love with Melbourne. The city is a gleaming, sun-kissed hive of smiling, bronzed people, a world in which all the girls are blond and jogging or Rollerblading along a riverbank as rowboats glide past.

We leave Gino's and cruise the length of Chapel Street, "which is kind of like Melrose in L.A.," according to Bana, then skirt the ritzy shopping district. Windows down, radio off—only the sound of two men chewing Dentyne accompanies Bana's commentary.

We stop at a park and watch some ducks being fed. It seems a little sedate for Hector of Troy. But the ducks aren't the draw for Bana. "It's a Formula One track. There's a race in three weeks' time."

He never planned on being Eric Bana the actor, or the comedian, for that matter. What he really wants is to be Mario Andretti. Between shooting movies, Bana can be found "fart-arsing around with my car, getting ready for a race." Although he has more than one, his favorite car is a fire-engine-red '74 XB Falcon coupe that he calls the Beast. He's had it since he was 15.

"Three of my closest friends—our relationship has been maintained because we've always worked on this car," he says. "The car has transcended itself. It has become a campfire."

But one day, during the Targa Tasmania rally in April 2007, he crashed into a tree. "I totaled it. After a two-year restoration, everything handmade. Oh, it hurt—yeah. Absolutely."

He falls silent for a moment, still mourning the Beast. We exit the F1 track and stop at a light. The Temptations' "My Girl" drifts from the car next to us. "It's a bashed-up thing in the corner of the workshop," he says. "It's sitting there, not being used, but it's still my emotional bedrock, my anchor." The Beast represents Bana's memories, good and bad, and he wants to preserve them, just as his father did before him. A Croatian named Banadinovich who worked for Caterpillar, he came to Australia at the age of 16 and kept a Thunderbird—also fire-engine-red—for 35 years. Bana's urge to preserve the past goes beyond the Beast. He prefers local stores to malls, for instance. "You want a piece of meat, you go to the butcher. You want a coffee, you go to the café which is not a chain," he says.

We drive and drive: past the fancy houses to the rough areas, past the railway station where Bana used to wait on the steps for his first girlfriend, and past his old school, where he says he once showed up drunk—prompting his mom to ground him for six months. "Yeah, I went through a little phase there. But I did a lot better than some of the guys I hung with, who have ended up dead or in jail," he says. Bana wasn't a star student: He had to repeat a year of high school. "It wasn't like I was busting to get into NASA or anything," he says.