CHICAGO TO NEW ORLEANS

934 miles; from $146/£116

Union Station is Amtrak’s hub in the Midwest – the start of several cross-country routes. Some of these go west – but the “City of New Orleans” train sets its sights on the south.

CHICAGO

Like New York, Chicago is a city where you might easily linger for days. Its Art Institute (artic.edu) is one of America’s greatest galleries, home to delights by Hopper and Seurat. You can max out every card you have in the shops of the Magnificent Mile. And though the Willis Tower (willistower.com) is no longer the world’s tallest building, the views it offers of Lake Michigan are enduringly spectacular.

Stay: The 21C Museum Hotel (001 312 660 6100; 21cmuseumhotels.com/ chicago); from £147

First leg: 10.5hrs; from $89/£71 MEMPHIS

The City of New Orleans takes almost half a day to carry you down through Illinois and (briefly) Kentucky – before rolling into Mississippi for a date with the “Home of the Blues”. Memphis is forever defined by its musical heritage – Elvis’s ghost holding court at Graceland (graceland.com), the Stax Museum (staxmuseum.com) telling a soulful tale, the bars of Beale Street awake until late – but no less exciting for all this giddy nostalgia.

Stay: The Peabody (001 901 529 4000; peabodymemphis.com); from £217

Second leg: 4.5hrs; from $34/£27 JACKSON

There is no precise geographical definition of the “Deep South”, but you have definitely crossed into it by the time you reach the Mississippi capital. The Mississippi Civil Rights Museum, a relatively recent addition to the map (opened in 2017), shares its block with the Museum of Mississippi History (mcrm.mdah.ms.gov). The state capitol is barely older. This Beaux Arts landmark – topped by its inevitable dome – only opened in 1903.

Stay: The Hilton Garden Inn Downtown (001 601 353 5464; hilton.com); £81

Third leg: 4.5hrs; from $23/£18 NEW ORLEANS

The titular city at the end of this particular railway line has a reputation as a party hotspot thanks to the annual February high jinks of Mardi Gras. But New Orleans is enthralling at any time of year – raucous and rabble-rousing in the many bars of the French Quarter, but in touch with another great strand of American music in the Jazz Museum (nolajazzmuseum.org) and the sacred space of Preservation Hall (preservationhall.com).

Stay: The Royal Sonesta (001 504 586 0300; sonesta.com/royal-sonesta); £191