IF YOU’VE HEARD of Sullivan County, it’s probably for its “Borscht Belt” days: the post-World War II decades immortalized in the film “Dirty Dancing,” when sprawling, country club-style resorts carpeted the lonely western foothills of New York’s Catskill mountain range. In the 1960s, the region was said to have more hotel rooms than any other county in America, but by the time Baby and Johnny mamboed into theaters in 1987, the resorts had all gone—doomed, in large part, by air travel’s growing viability as an affordable middle-class luxury. With them went the region’s cachet as a vacation spot.
Recently,...