Outside of Pompeii, what effects did the CE 79 eruption of Vesuvius have on the wider Roman Empire, in terms of sociopolitical, physical, and climactic effects?

Maritime traffic that had once docked at Pompeii now headed south to Stabiae (ironically, the place where Pliny the Elder died, but not wiped out to the extent Herculaneum and Pompeii had been). Within a year, the town had recovered not only the traffic it had previously serviced, but that lost by Pompeii, Herculaneum, and Oplontis. The price of wine shot up as the considerable vineyards surrounding Vesuvius were now off the market. Roman engineers laid down new roads along the coast, ironically, from Misenum (northern tip of the bay of Naples) to Stabiae, Pliny the Elder’s beginning and end points back in the summer of AD 79, in the expectation of returning prosperity.

How quick people were to hazard the area after the fact is an interesting question. “Even now the peak still menaces death,” in words of the poet Statius (45AD -94 AD).( Statius, Silvae IV iv 82-83) Born and bred in Naples, Statius moved to Rome as soon as he could. (bear in mind that he was looking for a patron, which he got, in the form of Titus's brother, the emperor Domitian.)

For others, however, the mountain rich soil and the area’s easy access to a world class harbor was simply too good to pass up. A hundred and forty or so years after the explosion, Dio Cassius can confirm that “[Vesuvius’s] out-lying heights support both trees and vines in abundance.”

He goes on, however, to say that “the crater is given over to the fire and sends up smoke by day and a flame by night; in fact, it gives the impression that quantities of incense of all kinds are being burned in it. This, now, goes on all the time, sometimes to a greater, sometimes to a less extent; but often the mountain throws up ashes, whenever there is an extensive settling in the interior, and discharges stones whenever it is rent by a violent blast of air. It also rumbles and roars because its vents are not all grouped together but are narrow and concealed. Such is Vesuvius, and these phenomena usually occur there every year.” (Dio Cassius LXVI 21 )

Then as now, people were more than willing to take the risk.