As you point out, people should not miss Ercolano. We went to both
Ercolano and Pompei 2 years ago. We were blown away by
Ercolano, where we could see charred beams in the ceilings, walk on
the mosaics of the ancient Baths, see a lot of restoration going on,
and generally get the feeling of being in a small Roman town much mroe
than you can at Pompei.
I also very much endorse your suggestion of visiting the fumarole near
Pozzuoli (named Solfatara), and the archeological dig of Cumae.