If you only have one night to spare in Sorrento you can still cover a lot of ground.
From Rome, start early by catching one of the first trains for Naples; once there, you can go to the Circumvesuviana station close by, which is where all trains going to the peninsula depart from. Stop at Pompeii about thirty minutes after leaving the station, and spend a few hours there before proceeding on. If you have not got a hotel, go straight to Sorrento proper and contact the local tourist center there. They have contacts all over the area, and will usually make the necessary calls themselves. Campgrounds are also present outside Sorrento town, but it can be quite a trek to reach some of them.
Little villages such as Meta or Piano di Sorrento can be excellent value for money, and are very well connected to Sorrento proper by the Circumvesuviana train.
The trains run all day, the last departure from Sorrento being at 11.30 pm.
Once you've settled in, you can do some shopping or relaxing on some of the beaches. If you have a vehicle you might want to consider driving dowm the southern side of the peninsula, along the famous Amalfi coast, but be warned that the drive is the most notorious in Italy, even worse than some Alpine roads, and it can take a fair amount of time due to traffic congestion.
The next day you can return to Naples via Capri, by catching a hydrofoil from the port of Sorrento, located at the bottom of the gorge in front of Piazza Tasso. After spending some time on the island, another fast hydrofoil ride will get you back to Naples in about forty-five minutes.
From the dock, the easiest thing to do is simply use a taxi to get back to the station; it's only a five minute ride from the port. Alternatively, if you've got a car with you, you can spend some time in Naples itself, as private vehicles are not allowed to disembark on the island of Capri.
The Italian goverment is currently building a fast train link between Naples and Rome, which should reduce the travelling time to roughly two hours, and which should (hopefully) be running by next year.