I would be grateful for recommendations for Puerto Vallarta, Acapulco, Guatemala City, Puntarenas, Cartagena, anything really outstanding.

Also, any options for non-cruise line organized excursions?

In Acapulco we did a private tour with Rosy ,went to the cliff divers, Cross on the hill and many other sights. The Fort is across from the port & you can do that on your own.
Guatemala we docked Puerto Queztel to a taxi Guide to Antigua
Puntarenas you can hire a guide.driver at the dock we just walked around the city & along the beach front right at the dock

Cartagena we did a ship's tour ...we found the pedlars very persistant ..they do not take "no thank you" for an answer