In Greek mythology, the Styx is a principal river of the Underworld—not a physical stream in Italy. It encircles Hades nine times; gods swear binding oaths by it; Achilles was dipped in it for invulnerability (except his heel).
Baia (Baiae), near Naples, was a Roman resort famous for volcanic steam vents, hot springs, and tunnels. Robert F. Paget's In the Footsteps of Orpheus (1967) proposed that the Oracle of the Dead at Baia—specifically a tunnel complex with a subterranean stream—was the real-world inspiration for the Styx myth.
Most classicists and archaeologists reject Paget's theory. The Baia tunnels are likely drainage or water-supply works for the Roman baths. The Styx remains a mythological construct—powerful, poetic, but not a geological feature you can visit in Campania.
Visit Baia for its sunken ruins (Parco Sommerso di Baia), temples, and volcanic landscape—not the River of Hades.