Mount Vesuvius--yes, the Mount Vesuvius that wiped out Pompeii-- is a great day trip from Sorrento.
Getting to Mount Vesuvius from Sorrento is pretty straightforward. One option is to book a spot on a tour bus. These can be secured in Sorrento. Another option is to take the Circumvesuviana train from Sorrento to the Ercolano Scava stop. There you can catch a bus Mount Vesuvius.
The main thing to decide is if you want to walk all the way to the top or take the bus almost all the way to the top and walk the remainder of the way. Either way, wear comfortable shoes! You‘ll be climbing so, sandals or ballerina/flats are not the best choices.
Also, note that there is an entry fee to Vesuvius national park. This entry fee is usually not included in the bus fare.
Once up top and in the park, you can take a lovely stroll around the crater. Vesuvius is still active so you might even see smoke!
Finally, be sure to sample the local wine -- Lacrime Cristi wine -- made out of the grapes that are growing on Vesuvius.