Your input on Naples

One month 'til Cefalú!
On Tuesday afternoon May 13, I will travel from Palermo to Naples, for three nights at the highly-rated Orsini46 B & B in the Santa Lucia area of Naples, near Plebiscite Square and the fishermen's area. I thought I would share my current plans for my visit and see if any of you Napoli-philes have some suggestions.
May 13 -- cab from airport to B & B, then poke around that general area of Naples and have a nice dinner nearby.
May 14 -- My day in Naples, including the Archeology Museum and wandering the streets and sites of Naples, using the RS walking tour. Would value your thoughts on the top few things to visit in Naples.
May 15 -- start at the Porta Nolana Market (I love markets!) near the train station, supposedly the most scenic, then catch a train to Salerno at about 10 am (under 40 min ride) and poke around Salerno and maybe Vietri al Mare for a few hours; then get a train or bus on to the ruins and museum at Paestum, that I understand are nicest in the late afternoon and early evening. Then a train back to Naples for dinner and the night.
May 16 -- a few more hours to wander or visit one site in Naples. Then I plan to catch mid-day hydrofoil to Sorrento for a few days, from which I will also visit the Amalfi Coast, Herculeum and Pompeii, and maybe Capri.)
My questions for you:
1. Does this plan sound good and reasonable to you?
2. Aside from the museum, what do you think are the very best sites in Naples, to be sure to visit?
3. Any recommendations for special restaurants for lunch and dinners in Naples? I will be on my own, so am more into excellent local food, friendly informal atmosphere and maybe some scenery, not fancy, very expensive or romantic!
4. Do any of you know Salerno and even Vietri al Mare? What to see in the former and does the latter merit the short bus ride and time to visit?
Grazie for any thoughts you might share, Larry