We’d been speaking with the two men for several minutes before anyone mentioned their great dane’s pink toenail polish. Its owners were very much a couple. One carried the Sunday New York Times; the other wore a cravat.

We’d stopped to ask them if they knew a good place to eat, as the surrounding neighbourhood contained a dizzying array of restaurants, including a Cajun place with a bloody-mary bar, a bistro that featured “French comfort food” and a likely-looking Thai establishment.

“Why is your dog wearing pink nail polish?” one of my nine-year-old twin daughters finally asked.

“Well, we tried magenta,” the man with the cravat deadpanned, “but it just wasn’t him.”

Kayaking America's Deep South

It might look calm... but there are monsters out there. Brian Schofield braves the gators of Georgia

• New Orleans: the complete guide

Mississippi cruise legend

The Delta Queen is an American institution, but after 81 years of service, her time is nearly up. Hurry aboard

The mountain music of North Carolina

On a serendipitous journey into the Appalachians, Stephen Bleach finds the sound of old America - plus more world music

• Serbia shines for the EXIT festival

On the USA blues trail

It’s America’s great musical journey. Stanley Stewart gets down and dirty from the Mississippi Delta to Chicago

• The girl's guide to glamour in Gotham (aka shopping in New York)

No, we were not in Greenwich Village or San Francisco, but rather in Asheville, North Carolina, nestled in the heart of Appalachia. And we’d arrived just in time. After two days in Dixie, I was beginning to regret my decision to lure my wife, our teenage son and twin daughters on a road trip into the South. Although I’d promised them an encounter with a unique part of America, so far we’d seen mostly strip malls, corporate headquarters and McMansions. The new South, I was beginning to fear, was no different from the rest of America.

Then we entered the Appalachian Mountains of western North Carolina, and it soon became clear that we had arrived in a place unlike any other in the United States. Asheville is a case in point. Although the darkly wooded hills surrounding it were full of Baptist churches, barbecue shacks and billboards threatening eternal damnation, the city itself (pop 72,000) proved to be an oasis of stylish liberalism with a distinctly Southern accent.

In addition to a diverse spread of restaurants, Asheville’s narrow streets offer an eco-chic boutique, a sustainable-clothing warehouse and a selection of pubs that would not be out of place in a Gloucestershire village: Jack of the Wood, the Green Man and the Thirsty Monk were all within a block of one another. Arriving here, you feel you’ve discovered something increasingly rare in homogeneous America: a regional city with a personality all its own.

We had begun to understand we’d left striving, modern Dixie behind earlier in the day, as we followed fog-shrouded Route 74 out of prosperous but bland Charlotte. Our first stop was Chimney Rock, a stunning formation rising from the surrounding forest. On approach, it looks less like a chimney than a particularly obdurate mushroom.

After lunching on barbecue ribs beside a turbulent little river that had only a week earlier washed away some picnic tables from our terrace, we tackled the surprisingly gentle 300ft climb up to the summit. The rock’s naked promontory boasts views of surrounding Appalachia that are rumoured to range up to 75 miles, though our vista was considerably less due to encroaching thunderclouds. The hiking trails that vein the park below are well worth the effort, particularly the Hickory Nut Falls route, which leads to one of the East Coast’s more beautiful waterfalls.

Next came the Biltmore House, the ancestral seat of the Vanderbilt dynasty and the largest private home in America. Situated just south of Asheville, it was built by George Washington Vanderbilt, grandson of the shipping magnate Cornelius “the Commodore” Vanderbilt, America’s first great robber baron. George was a sensitive soul who lacked his forebear’s cutthroat business acumen and decided instead to devote his life (and redoubtable fortune) to the arts. The house he built, which was officially opened on Christmas Eve, 1895, is set on 8,000 acres of rich Southern backwoods, and the 175,000 sq ft structure appears to have been transplanted in its entirety from the Loire Valley.

The basement is the house’s most interesting floor, because here you get a sense of what makes Biltmore distinctly American (the other floors being a peculiarly European mishmash of Flemish tapestries, Chippendale furniture and Renoir paintings). There is one of the nation’s oldest bowling alleys, an 1890s “state-of-the-art fitness room” and some of the first indoor toilets to hit the South. There are five distinct gardens surrounding the house, designed by Frederick Law Olmsted (best known for planning Central Park), and they’re all stunning. There is also a working winery and a model farm.

After spending the night in Asheville, we went to Black Mountain, a few miles east of the city. Home of a famous school of American poetry, it proved a quaint village of shops, beautiful homes and interesting-looking people — the sort of place you want to move to immediately, but are ready to leave after an hour.

Times recommends

• Friday: latest flight and airport news
• Ski guide school in Whistler
• The best festivals in France, 2010