Torre del Greco as a base for Pompeii, herculaneum and vesuvius

It would be fine. Lower key than Naples but still not a quiet and tranquil town.
Good places to eat.
it's a suburb of Naples so lots of overlap between the feeling/atmosphere of the two places.

Thank you I was thinking this place would be a tranquil oasis after a day at the sites rather than staying in the city itself. Will probably not spend much time in town other than dinner
https://www.casinadegoyzueta.it/

We were on Campania in January and based in Pompei with a car. We visited all those sites, did a trip into Naples for the Archaeological Museum, and drove to visit Positano and Sorrento. The town part of Pompei is a regular town with a main square, big church and local dining and shopping. It was convenient to have that close by without the congestion of a big city. I suspect Torre del Greco will be similar. Good luck with the trip!

Month of year? You might have the largest list of lodging options in Sorrento. I wonder if Torre del Greco (TDG) has a beach. I don't remember seeing TDG ever mentioned on this board before. I have seen Massa Lubrense, Meta, and Sant Agnello mentioned, but have not been in any of them. The walking distance to transportation to Naples from your hotel seems important. The Circumvesuviana stops right under the main train station in Naples, but can be staggeringly crowded. Does a bus from TDG stop in the Naples train station's big bus plaza?

Be aware that Herculaneum Scavi is a 12-15 minute steep downhill walk from its Circumvesuviana stop. Pompeii Scavi is right at its station.

It's about 25 minutes from Torre del Greco by train. it's very convenient and far less touristy than Sorrento.
Yes Torre del Greco has several beaches, but do you even want to go to the beach?
Torre del Greco has many, many hotels at far lower prices than those in Sorrento.