My suggestion is to drive from Apulia to Paestum and perhaps spend the night. Other than the ruins and the museum, there are beaches and mozzarella producers to visit in the area. Then take the short drive to Salerno to return the car and take a bus or ferry to the town of Amalfi. I’ve stayed in both Positano and Amalfi and enjoy Amalfi more because it’s not as touristy, less expensive and a transportation hub (bus and ferry) to get to Positano, Ravello, Praiano and just about anywhere else on the coast. You can even take the ferry to Capri.
In Paestum I stayed at the wonderful B&B La Chora di Paestum. The website is only in Italian but I reserved it and read the English descriptions at Booking.com. The owners recommended Bistrot 73 on Via Tavernelle - great food at reasonable prices. In Amalfi I stayed at the 6 room Villa Annalara. Large rooms and a terrace with marvelous views of the town and the sea. Wonderful food at Ristorante Il Tari, midway between the Villa and the Cathedral.
If you’re going back to Rome, easiest way to do it is to return to Salerno and take the train.