No, there's no ferry service to Praiano, which is why I wouldn't choose it as a base either. Positano is OK but I couldn't personally do it for a week, and it's sort of a pain to do Pompeii from there. Ferry service is more frequent to Capri from Sorrento, and more reliable than from Positano as rough seas can make it temporarily unsafe for boats to dock there.
I like Chani's suggestion to split your week between Sorrento and another location on the A.C. Although not everyone's cuppa, we liked Sorrento and thought the view of the Gulf of Naples from its perch above was plenty scenic.
One caution? Most of us would advise staying close to your airport of departure the night before an international flight. Having had to get up at serious o-dark-thirty and take a cab to Naples for an early plane out (trains from Sorrento not running at that hour), that's not an experience I'd repeat again.