Thanks to all for your replies.

The Artecard is strange: the 3-day card includes full use of public
transit systems, while the 7-day card does not include any
transportation at all! But it's a good tip, and I'll see which one
best meets my needs. Maybe I can combine it with a separate multi-day
transit pass...

By nightlife in Naples, I just meant going out to dinner, and seeing
sights that are illuminated at night, and perhaps sitting and chatting
at a sidewalk cafe or doing a passagiata. That's how I usually spend
my evenings when I travel; I'm not into clubs or bars or dancing.....

I thought lodging in Positano would be considerably more expensive
than Sorrento; hence my idea to do it as a daytrip (or two). But
moving on down there for a couple of days would definitely be
preferable if I can fit it into my budget, since there is quite a bit
along that coast I would like to see....