Puerto Limon is a port city, period.
Puerto Limon is a port city, period. Unless you are there solely for business meetings, there is no reason to spend the night there. The water is inaccessible, the city itself seems quite dangerous, it is not beautiful, and the food is processed, pre-packaged type food - not authentic, not healthy, not tasty. We spent 2 full weeks in Costa Rica and Puerto Limon is the one city that we could not wait to leave, and regretting choosing to spend a night there.
It is interesting, however, to drive though the town to see the port, the ships, the massive scale of the mono-cropped banana farms, and the miles and miles of shipping containers. Drive through, but stay on either side of the city. Cahuita is less than an hour and WONDERFUL!