Saugatuck is chock-full of B&Bs and inns. Try Twin Gables Inn (269 857 4346, www.twingablesinn.com ; doubles from £68, B&B), which overlooks Lake Kalamazoo and comes with complimentary bicycles. More information: 269 857 1701, www.saugatuck.com .

The alternatives: Chicago is a key hub, with trains to New Orleans, Los Angeles, Seattle, Memphis and New York, so there are potential stops in all directions. Our favourite is the lovely Michigan University town of Ann Arbor, with its bright, bustling, bookstore-filled downtown.

LOS ANGELES
Start from: Union station, a pretty, palm-tree-fronted, Spanish mission-style building: imagine the Alamo as a rail terminus.

All aboard for: Palm Springs , across the desert on the marvellously named Sunset Limited. This sprawling city has had its ups and downs, but now it’s once again a fashionable retreat for Angelenos seeking clean air and a little golf or tennis. Palm Springs isn’t about chasing around in the heat. It’s about finding a decent resort, lounging by the pool, admiring the striking 1950s desert-modern architecture of places such as the Holiday Inn and Movie Colony Hotel, and maybe exploring the San Jacinto mountains and canyons. You can take the Aerial Tramway up to a cool 8,500ft and do some hiking, or sign up for Red Jeep desert tours (760 340 2345, www.red-jeep.com ). I saw my first wild tarantulas with them.

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It’s about 2½ hours from LA, £20 return. Book a cab to pick you up at the station - downtown is about four miles and £8 away: try VIP Express (760 322 2264, www.vipexpresstaxi.com ). Stay at the excellent Desert Riviera (760 327 5314, www.desertrivierahotel.com ; doubles from £80), which harks back to the 1950s in style but is bang up to date with service and facilities. More information: 760 778 8418, www.palm-springs.org .

The alternatives: you’re spoilt for choice. North on the Coast Starlight gets you to wealthy Santa Barbara, San Luis Obispo for Hearst Castle, Oakland for San Francisco, and, eventually, Seattle. The ride south, on the beach-hugging Pacific Surfliner, takes you to the perfect California climate of San Diego (stopping at Fullerton for Disneyland).

WASHINGTON DC
Start from: DC’s Union station, and take your time. It’s a vast railroad palace, with shops, restaurants and bars, as well as the odd train. I like sitting at the bar at B Smith’s, which is tucked away off the East Hall. Its palatial dining room is a national landmark - it was once the Presidential Suite, where the top man and his entourage would board their train. All aboard for:Charlottesville, Virginia, one of America’s most fascinating and comfortable cities. It’s a college town, and the University of Virginia is a Unesco World Heritage Site, thanks to its collection of classically colonnaded American architecture. The university was Thomas Jefferson’s creation, and a visit to his home at Monticello (434 984 9822, www.monticello.org ; adults £7.50, 6-11 £4), two miles out, is on every visitor’s itinerary. The third president was a fascinating character, and it’s well worth the trip.

Elsewhere, it’s a lively place, with a wide range of restaurants, interesting shopping, museums, galleries and plenty of entertainment. Drink or dine at the crepuscular, candlelit C&O (515 East Water Street; 434 971 7044, www.candorestaurant.com ), once a railroad building.

The train to Charlottesville, running through beautiful Virginia countryside and shadowing the Blue Ridge Mountains, takes just under three hours and costs from £38 return. Stay at the lake-side Boar’s Head Inn (434 296 2181, www.boarsheadinn.com ; doubles from £75), a first-class country resort, with golf, tennis and good food. It’s a two-mile, £8 cab ride away. More information: 434 293 6789, www.pursuecharlottesville.com .

The alternatives: if you fancy mixing the senate with sand, trains run from DC to Newport News, an hour’s bus ride from Virginia Beach, a booming seaside town that claims to have the world’s largest pleasure beach. A good stop for surfers, too - it plays host to the East Coast Surfing Championships.

Buying tickets: you can book on www.amtrak.com or at any Amtrak station. The fares quoted above are for travel in September/October. For longer train tours, International Rail (0870 084 1410, www.internationalrail.com ) and The Travel Bureau (08448 156212, www.thetravelbureau.co.uk ) sell 15-and 30-day national and regional passes (from £160 for 15 days in the northeast region), which are excellent value.

CROSS AMERICA BY RAIL
The California Zephyris one of the world’s great trains, going from Chicago to San Francisco by way of America’s heartland and the high plains of Colorado, then climbing into the Rocky Mountains via the Oregon Trail. Pioneers came this way, as did gold prospectors and America’s first continental telegraph. After Salt Lake City, you cross Bonneville Salt Flats and the beautiful Sierra Nevada.

The Southwest Chiefalso travels between Chicago and the Pacific, following part of the Santa Fe Trail first used by Native Americans, Spanish conquistadors, wagon trains and stagecoaches. You cross the Mojave Desert, one of the hottest places on earth, and pass Dodge City’s famous Boot Hill burial ground. From the station in Williams, Arizona, you can travel to the Grand Canyon by steam train.

The Coast Starlightoperates between Seattle and Los Angeles, via Washington, Oregon and California. It passes some of America’s highest mountains, such as volcanic Mount Hood, and the forests and waterfalls of Twin Peaks country. Beyond San Luis Obispo the train runs on tracks set high on cliffs, with wonderful views of the Pacific surf and beaches.

John Pitt + USA by Rail by John Pitt (Bradt £14.99) covers 500 destinations and 25 long-distance rail journeys. The routes above can be found on www.amtrak.com . Also useful is Man in Seat Sixty-One (www.seat61.com/UnitedStates.htm )

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