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Museo Archeologico Nazionale
Museums
The single most important collection of Roman material anywhere. Nearly everything portable from Pompeii and Herculaneum ended up here: the Alexander Mosaic from the House of the Faun, wall paintings lifted whole, bronze sculpture, glass, surgical instruments. The Farnese collection adds the colossal Farnese Bull and Hercules. The Secret Cabinet holds the erotic material, kept locked away for most of the museum's history.
Go here before Pompeii, not after — the site makes far more sense once you have seen what came out of it.