From October 24 to 27, Japan’s roadways will resonate with the rumble of the Alfred Dunhill Rally Nippon—a 621-mile, scenic round-trip circuit from Kyoto to Shikoku, which tracks some of the country’s quintessential cultural sites. Participation is by invite only, and only the most qualified car collectors are considered.

Limited to 70 entries, each classic car must predate 1975—no replicas allowed. Those competing this year range from a 1928 Bugatti Type 37 and a 1929 Bentley 4½ Litre Blower to a Maserati …