Luxury vintage car tour: Driving Melbourne to Mornington Peninsula in a 1957 Chevrolet Sport Coupe

When I'm on the road I spend a lot of time overtaking, inching up the right lane trying to take every advantage to shave time off my drive. Lucille, on the other hand, is a left lane kinda gal. She's happy to watch the flustered over-takers slide past, she's as focused on the scenery as they are on the clock.

Lucille is a 1957 Chevrolet Sport Coupe, a two-tone aqua beauty with white-wall tyres that is fondly known as "Detroit Iron", a reflection of a time when America made great cars not just empty slogans.

Lucille is one of the cars at d'Luxe Classic Car Tours based in Melbourne and run by John Frostell who purchased the Chevy in the 1980s and spent nearly three decades bringing her back to factory standards.

"Something about the pace of a classic car trip lends itself to chatting, it is nice to just hit the road and talk about the region you are in, and to get to know each other," says Frostell, our driver and guide on a day trip to the Mornington Peninsula, my two boys lounging on Lucille's generous grey-and-aqua backseat; windows cracked as the "natural air-conditioning".

Our first stop is the Eagle at Arthur's Seat, another mode of transport where time is hardly of the essence. The Eagle is a cable-operated gondola system that hauls passengers up over the Arthurs Seat State Park high over a canopy of casuarina with views across the Peninsula beaches. While we ride the Eagle, Frostell guides Lucille up the snaking road to meet us at the top, where a crowd has gathered to admire the classic car. When you ride with Lucille you can't be shy, you are travelling with a celebrity and people stop to take photos, ask questions or just admire her steely curves. We clamber in and drive off to our next stop: the Ashcombe Maze & Lavender Gardens where the boys stretch their legs as we hunt through the hedges and woodlands to tick off the various hidden fairies and gnomes.

Lunch is at Montalto, where Lucille looks at home parked among the many artistic creations of the Sculpture Trail. Montalto runs an annual sculpture prize where the winner ends up added to the art-among-the-vines permanent collection.

Classic or not, being on a car trip with a stranger is close quarters but with Frostell you are not trapped with some car nerd. Over a glass of rose – and some amazing fish wings with chilli and black vinegar as well as roast cauliflower, grains, pistachios, pickles and yoghurt – Frostell is a wealth of knowledge about the region, the winery and a range of other topics; great company as well as a good guide. He says he loves the bespoke nature of his business where every day is different and is "just as happy to visit the Silo Art Trail as I am drive you up to get a burger in Avenel".

After lunch we drive along some of the Peninsula's switchback roads and pay a visit to Port Leo beach all to a soundtrack of classic jazz from Lucille's mid-century heyday. Frostell opens the car's boot that could easily hold two extra passengers and produces a Frisbee for the boys to play with on the sand.