After racing down a two-mile runway, a van carrying top airport officials rattled onto a patch of asphalt overrun with tall swaying grass, wildflowers and herbs. “Ah, smell that oregano,” said Antonio Maria Vasile. “It’s wild fennel if it’s anything,” replied his boss, Marco Franchini.

“No, it’s oregano,” grumbled Mr. Vasile as Mr. Franchini stepped out of the van and announced: “Here we are. The Space Port.” Grottaglie, a medieval town known primarily for its handmade ceramics, is getting ready for liftoff. In July, Italian aerospace companies signed an agreement with Virgin Galactic to take space tourists with about $250,000 to burn on suborbital flights offering vistas of the curvature of the Earth and about five minutes of minimum gravity.