In a Mazda MX-5 Miata convertible, Dana Dickey zooms the ridges, ravines, and switchbacks of Hawaii's Valley Isle

My mission: to boldly go where no man has gone before—sort of. Let me explain. On previous visits to Maui, I have wondered about the sections of road marked by a dotted or skinny line toward the bottom of rental car company maps, some labeled "four-wheel drive only." These are stretches where, island rumor has it, rental car companies won't rescue less rugged vehicles when they get stuck. I was intrigued by a wilderness in the middle of a Hawaiian destination purpose-built for visitors, from the golf courses in Kapalua up north, to the glittering resorts in Wailea to the southwest, to the up-country bicyclist mecca of Haleakala volcano. Could there still be an authentic Hawaii along these dotted lines, a windward length of coast less traveled—and could I take it on in my vehicle of choice, the spunky Mazda MX-5 Miata? Guidebooks, the Internet, and even locals told me (a) Try it, (b) No, don't try it, and (c) Well, you might be okay unless a big storm washes out the road…So I decided that the only way to find out was to drive one of these stretches of road myself. Along the way, I'd seek out a wild and woolly Maui, a land of farms, ranches, and open grassland.

Day One, 80 miles: Kahului to Haleakala Crater
At noon, I picked up my car near Kahului airport and drove east on the main road, Haleakala Highway. Within ten miles I was heading through sugarcane fields and enjoying how the car's low center of gravity hugged the road as it zipped past the ubiquitous pickups and SUVs. I was doubly glad to be in my little open sports car, most immediately because the chance to smell fresh sweet grass and loamy earth is one of the peerless joys of a convertible, and secondly because my ride gets 30 miles to the gallon—more than twice the fuel efficiency of some SUVs.

At 3,000 feet, I felt my ears pop. I spotted a family-run roadside store and pulled over to ask which of the small unmarked dirt turnoffs I should take to get to my first stop, a farm that exports artisanal cheeses across the country. I bought a Häagen-Dazs bar, and as I unwrapped it, a pop song came on the radio that sounded as though a DJ had mixed the Clash with a ukulele backbeat. I drove along, carelessly letting pieces of vanilla ice cream and chocolate blow all over my face. My blissful messiness was interrupted by a weather warning: An offshore storm could possibly hit Maui within the next couple of days. Gloomy visions of my sleek little car getting sucked into a sinkhole on a deserted stretch of highway made me miss my turn.

I circled back around on Haleakala, or Highway 37—whose name changes to Kula Highway as it snakes uphill—turned right, and followed a circuitous bumpy road for four miles to the end of dusty Omaopio Road. Surfing Goat Dairy is a modest-looking affair—a wooden store and a couple of large barns surrounded by pastures of smelly goats. "They're just musky like this in mating season," said my guide, as she led me through the moist earth between pens. "The males pee all over themselves. Then at the end of breeding season in October, they clean themselves up." As she spoke, billies craned their necks through the fence. I felt a tug and caught a nine-month-old that had squeezed through the fence far enough to get a mouthful of the hem of my dress. The big cheese at the dairy farm is a five-year-old curmudgeon named Hansie, who menaced us with two-foot-long horns until the guide sprinkled water on his head. As I walked away, goats ran up to me, thinking I had food. By the time I reached the parking lot, the dairy owners had come running too, but to my car. "Looks like a Corvette," said the lady of the land. My full-figured Hawaiian guide narrowed her eyes. "But too small," she said. "Definitely not for deliveries."