We decided to move from London to New York. Writers can write anywhere, I thought. It's a privilege. Why pass up that freedom? So last August we brought our dogs over on the Queen Mary 2. I heard that Ashleigh and Pudsey – winners of Britain's Got Talent 2012 – were on the voyage before ours, and that Pudsey had been allowed to sleep in Ashleigh's cabin. Our dogs had to sleep in kennels. I found the injustice intolerable. Still, the voyage was grand and exciting.
Then we arrived in New York and everything started to go wrong. There was Hurricane Sandy, followed by a winter that felt like it was injuring your bones. London winters are long resigned sighs, but in New York they are long sharp yells. I was homesick, discombobulated and writing badly. Every bureaucratic problem and family difficulty felt agonising. We were alone in a place that's amazing when you're excelling, but unforgiving when you're out of your depth. By December we were talking about going home.
Instead, we started planning a road trip. I would stare for hours at Google maps – at Yellowstone Park and Old Faithful and the Rocky Mountains and Martha's Vineyard and Niagara Falls. A road trip! All of America was on our doorstep. It was part of the reason why I wanted to move here. Americans don't think twice about undertaking epic drives. We could find beaches for our dogs to run on. (In New York, dogs are only allowed off the lead before 9am and after 9pm. I was getting sick of taking Floppy and Josie to Central Park and running frantically alongside them while holding their leads to give them the illusion of freedom.)
A road trip is the only way to have a humane holiday with your dogs in America. Amtrak trains won't take them for some crazy reason, and the only way to avoid putting them in with the checked baggage on the plane is to get an anxiety note from your psychiatrist – which is something I'm definitely willing to explore.
The impending trip began to take on a massive significance for me. It was make-or-break – the thing to make me fall back in love with America.
And so, on 23 March, as the New York winter rages relentlessly on, we hire a car and head south, down the eastern seaboard, to Georgia. This is the least ambitious of the great road trips from New York. North will be bitterly cold, west will take forever, Savannah, Georgia, is only about 13 hours away. It is me, my wife Elaine, son Joel, and Floppy and Josie. We turn on to the New Jersey Turnpike, with its severe smoke-billowing factories.
I pull out all the emotional stops by putting on Bruce Springsteen: "Down the Shore, everything's all right…" And I suddenly feel very excited. "It's a town full of losers, and I'm pulling out of here to win!" he sings, as we head along the I-95. Infected by his energy I speed up to 68mph. My GPS sets off a warning bleep, so I go back down to 65.
The highway is insanely boring. But after the drama of New York, there's something calmingly cocoon-like about being in a car with your family. It feels quiet and safe.
We arrive at Annapolis, Maryland. It's full of ancient rickety inns in pretty cobbled districts but we can't find one willing to take the dogs, so we eat at a lovely steak place called Lewnes' Steakhouse and then get back on the highway, and keep driving south, through Virginia, and on to Fayetteville, North Carolina.
Objectively, Fayetteville is not great. It's basically a vast strip of chain restaurants and motels serving Fort Bragg, with its 60,000 or so troops, a mile away. But I love Fayetteville. I have a personal reason for loving it. This is where, 10 years ago, I discovered the existence of Goat Lab, the secret building inside which special forces soldiers tried to kill goats just by staring at them. I ended up writing a book about it – The Men Who Stare at Goats – and ever since I've idealised Fayetteville and towns like it as places where fantastic mysteries unfold everywhere, and you just have to be lucky enough to spot them.
We have dinner at a branch of Red Lobster. Every other booth is occupied by soldiers and their loved ones. They all have the same look – immaculate, polite, quiet. I don't see much talking. Perhaps these are goodbye dinners and they're about to be shipped off somewhere abroad. I am loving every minute of this journey through the strip-mall shadowlands. Which is easy to say because I'm not the one being shipped off. But American road trips aren't just about the picturesque destinations – they're about finding yourself in a random Red Lobster in the middle of mournful goodbyes.
The next morning we drive to Charleston, South Carolina, which turns out to be beautiful, like the south of France. There's a cool sea breeze and grand 1900s mansions and cobbled roads. I could live here, I think, but then I order a sandwich at the Bull Street Gourmet deli and it takes the guy about 20 minutes to make, so I decide I couldn't live here. We stay at a sweet hotel – the Kings Courtyard Inn – where they're doing that southern thing, where all the guests are supposed to meet and chat and drink sherry before dinner. We don't attend because we're introverted and find it overwhelming to meet strangers on holiday. Instead we walk along the seawall and eat at the fantastic, clapboard Hominy Grill. I have the shrimp and grits and collard greens – the greatest greens there are. I now understand the difference between Waffle House grits and proper grits. Next morning we drive an hour south to Savannah, Georgia.
We stop at the Bonaventure cemetery – Spanish moss-draped, grand and crumbling and eerie – and sit on Johnny Mercer's grave, like tourists do. Small intrigues are everywhere – like the signs on some graves that say, "Do Not Service". Maybe the families of the dead want to keep them tidy themselves. Or maybe the dead people did something bad.
In town we walk the dogs on the seafront, passing anti-slavery sculptures. Savannah is more liberal than much of the south – historically so, and also because of the art school here. It's that incongruous combination – art school and total otherworldliness – that makes Savannah so amazing. It's at once aesthetically like nowhere on Earth, and also culturally like Manchester in the 1990s – interesting clubs and galleries and underground cinemas. Charleston, for all its loveliness, seemed a little more spotlessly clean.
The antebellum part of Savannah is a huge chunk of the place, which is nice. (I've got a memory of nearby Macon being basically an antebellum street surrounded by acres of decidedly postbellum strip-malls.)
Savannah comprises 24 Spanish moss-draped squares. Many have ostentatious centrepieces – obelisks and gazebos and increasingly showy fountains – each seemingly built to outclass the others, like an escalating cold war of water features. We pass grand crumbling houses with their histories of murder and intrigue. Practically every Savannah mansion has had – at some point – an ivory-handled pistol fired in anger or jealousy by a local luminary spiralling out of control. John Berendt, the author of Midnight in the Garden of Good and Evil, puts Savannah's oddness down to its separateness: "Eccentrics thrived like hothouse plants tended by an indulgent gardener. Every nuance and quirk of personality achieved greater brilliance in that lush enclosure than would have been possible anywhere else in the world."
Elaine books dinner at a place called Elizabeth on 37th. She says eating there is a great Savannah tradition. I look it up on the internet. It's won awards – too many awards. I realise in horror that it is fine dining. So I go with enormous reluctance. And I'm really wrong. It's great. The restaurant is in the front room of a slightly dilapidated 1900s mansion, giving the grandeur a kind of spookiness, as if someone will emerge from the parlour any moment to say, "You're probably wondering why I've gathered you all together."
Our waiter has beads on his wrist. "What are they for?" Joel asks. "Are you a Hare Krishna or something like that?"
"Something like that," he replies. He starts to say something else. Then he stops. He glances around, and furtively pulls a photograph from his pocket. "He gave them to me," he whispers. It's a picture of the Dalai Lama. Then he shows us something else – his invitation to last year's Nobel peace prize ceremony, where he was a nominee for doing some big clean-water project with the Dalai Lama.
He smiles. "Only in America," he says, "would your waiter be a Nobel Peace Prize nominee."
And finally on south to the Sea Island resort . We had thought that, after all the driving, we would want to stay somewhere fancy and relaxing for a few days. This is a bit of a mistake. The grand lobby is full of massively self-possessed preppy Ivy-Leaguers wearing chinos and draping their tennis racquets over their shoulders, laughing and being basically excellent. I feel like I have to dart from the shadows to the escalator.
So we end up spending our days at nearby St Simons' Island, a sweet resort with huge beaches that the dogs get to run around on. It's not that well-known. Even people in Savannah – only 80 miles away – told us they had never been. But it's a great little island – clapboard, friendly, unpretentious and with lots of brightly coloured bucket-and-spade shops. They're complaining about a cold snap, but they have NO IDEA what a cold snap feels like, having not spent the past four months in New York. It's perfectly warm and lovely. I manage to wear shorts, albeit only for a few hours.
The dogs gallop along the beach, amazed that they can. We eat at a roadside soul food place – the Southern Soul Barbeque, which is endearingly weird and shack-like, with sand-covered families crowding into long benches as the sun goes down. It's a lovely thing to do on our last night before the drive back to New York.
When we arrive back in the city, it is spring. I go for smoked salmon at Barney Greengrass, "The Sturgeon King" in the Upper West Side, and I suddenly realise that I love it here.
• British Airways (ba.com) flies from Heathrow to New York and back from Atlanta from £572. Seven days' car hire (see ba.com/avis) costs from £429