"No--Pompeii is no longer a buried city. It is a city of hundreds and hundreds of roofless houses, and a tangled maze of streets where one could easily get lost, without a guide, and have to sleep in some ghostly palace that had known no living tenant since that awful November night of eighteen centuries ago." (Page 329)

Twain writes of Going to a town called Annunciation prior to his climbing Mt. Vesuvius. Torre Annunziata is the only locale I can find nearby Naples that fit his description.

Torre Annunziata is a city and comune in the province of Naples, region of Campania in Italy. It is located on the Gulf of Naples at the foot of Mt. Vesuvius.
https://en.wikipedia.org/wiki/Torre_Annunziata

Sam and companions climbed Mt. Vesuvius August 9th or 10th. while the Quaker City remained in Quarantine at Naples. Mark Twain Project: Quaker City Itinerary

The Vesuvius Observatory is the surveillance centre for monitoring the three volcanoes which threaten the Campanian region of Italy: Mount Vesuvius, Campi Flegrei and Ischia. Founded in 1841 on the slopes of Mount Vesuvius (the operative center is now based in Naples) by Ferdinando II di Borbone, king of "Due Sicile", it is the oldest volcanology institute in the world.
https://en.wikipedia.org/wiki/Vesuvius_Observatory

Herculaneum (in modern Italian Ercolano) was an ancient Roman town destroyed by volcanic pyroclastic flows in 79 A.D., located in the territory of today's commune of Ercolano, in the Italian region of Campania in the shadow of Mount Vesuvius.

The Real Teatro di San Carlo (English: Royal Theatre of Saint Charles) is an opera house in Naples, Italy. It is located adjacent to the central Piazza del Plebiscito, and connected to the Royal Palace. It is the oldest continuously active venue for public opera in Europe, opening decades before both the Milanese La Scala and Venetian La Fenice theaters.
https://en.wikipedia.org/wiki/Teatro_di_San_Carlo

The Upper Crust of Naples

The Royal Palace of Naples is located in central Naples, southern Italy.
It was one of the four residences near Naples used by the Bourbon Kings during their rule of the Kingdom of Two Sicilies (1730-1860): the others were the palaces of Caserta, Capodimonte overlooking Naples, and the third Portici, on the slopes of Vesuvius.
https://en.wikipedia.org/wiki/Royal_Palace_of_Naples

Castel Sant'Elmo is a medieval fortress located on a hilltop near the Certosa di San Martino, overlooking Naples, Italy. The name "Sant'Elmo" derives from a former 10th-century church, Sant'Erasmo, shortened to "Ermo" and, finally altered to "Elmo". It presently serves as a museum, exhibition hall, and offices.
(Wikipedia entry apparently deleted).

Lago di Agnano or Lake Agnano was a circular lake, some 6½ km in circumference, which occupied the crater of the extinct volcano of Agnano 8 km west of Naples, Italy. It was apparently not formed until the Middle Ages, as it is not mentioned by ancient writers; it was drained in 1870.