Near the House there is the typical Restaurant/Pizzeria/Bar (all in one) L’ARCHETTO, just 100 meters far from the house, on the main Street for Sant’Agnello center, at the first cross on the left. It is very typical restaurant, frequented by locals.
On Corso Italia, in the cross with Via San Giuseppe, there is Panificio DE PALMO, it is a good bakery, with Pizza to take away or eat inside on the tables (absolutely not expensive), preferred by locals.
Marina Grande in Sorrento is a great place to eat fresh fish. I think the best are DA EMILIA, just on the beach (preferred by tourists) or DELFINO just on the sea (preferred by locals).
The best beach by car is Nerano, Marina del Cantone with free and private beaches. 20 minutes by car far from La Terrazza. It is better in the early morning. Here you could to rent a boat for a day.
2 km walking from the house is the sandy beach Sant’Agnello La Marinella.
The beautiful beach club, just in front Capri is La Baia delle Sirene in Massa Lubrense (15 or 20 euros per person)
If You would like to visit Capri I suggest you a cheapest tour: http://www.sorrentoexcursionscenter.com/excursions/17/capri-island-tour.html with transfer included from La Terrazza.
You could to go without Tour Operator too. In the main square of Sant’Agnello, near Mama’s Bar, is the bus stop to Sorrento Port (ticket 1,20 €). From Sorrento to Capri the best and cheapest boat is Caremar (14,50 euros one way) start at 9.20 from Sorrento.
In Capri I suggest you soon, the tour of island and the visit at Blue Grotto. Than you could to visit Anacapri by bus from the port, or Capri center by cable car from the port.
In Capri we have a preferred restaurant on Marina Grande Port: L’Approdo. 10% off for our guests (say at Monica the owner, you are Michele guests).
To visit Pompeii I think is better to move by train from Sant’Agnello to “Villa dei Misteri” station, just near the ruins (25 minutes by train, 2,20 euros the ticket).
To visit Mount Vesuvius, I suggest you to visit by your car, If you haven’t it, every hours from 9:00 am to 3:00 pm shuttle bus “Busvia del Vesuvio” departing from the train station of Pompeii-Villa dei Misteri (20 euros per person).
For Naples is better to move by train to “Napoli Porta Nolana” station, just near the center. I suggest you to visit “Chiesa di San Severo and Cristo Velato museum” and eat pizza at Pizzeria da Michele. You could to come back in Sorrento by hydrofoil from Molo Beverello (Piazza Municipio).
To visit Amalfi Coast by your car, I think is better go until Vietri sul Mare, (I love Cetara), than come back by speed way A3 to Castellammare di Stabia. I suggest to stop in Positano, Amalfi, Ravello (Villa Cimbrone), Minori (visit De Riso pastery) and Vietri sul Mare (famous for ceramic factory).