While restoring the 1887-vintage Old Taylor Distillery in Frankfort, Ky., Will Arvin and Wes Murry, partners in the business, discovered abandoned train tracks on the property and a passenger depot once used by visitors arriving to tour the bourbon works. When it reopens in the fall, after a 40-year hiatus, as Castle & Key Distillery, the gin and bourbon brand will use the restored Taylorton Station as a museum, tasting room and the gateway to distillery tours. The 113-acre estate was established by the bourbon legend Col. Edmund Haynes Taylor Jr.

“It was a little like Pompeii,” said Mr. Arvin. “The magic of the place is that Col. Taylor was the visionary who figured out bourbon tourism was a cool thing.”

Now, it’s not just bourbon, but gin, rye and even limoncello leading a new wave of spirits-driven travel. As with food, wine and beer, traveling to the source for booze has exploded alongside the boom in craft distilleries, up 26 percent from 2016 to 2017, according to the American Craft Spirits Association. It currently identifies 1,600 craft distilleries, defined as those producing less than roughly 315,000 cases annually.

Small distilleries commonly open tasting rooms and offer tours as a way of marketing on a meager budget. Those start-ups are reimagining the ways they engage visitors, offering spirits festivals, mixology classes, concerts and other activities. Meanwhile, major brands are investing heavily in entertaining visitors with destination architecture, blending workshops and interactive exhibits.