Gorgona is a destination in itself, not a base for exploring the region. The journey to get here takes most of a day, and the park's accommodation and guided structure make it unsuitable as a launching pad. That said, two destinations are worth knowing about.
Gorgonilla. A small uninhabited island visible from Bahia Cocal beach on Gorgona's west coast. Boat trips can reach it, and snorkeling around its reef is excellent. This is effectively an extension of a day on Gorgona rather than a separate destination.
Guapi. The nearest town on the mainland, about five hours by boat. It is the transit point for most visitors and worth an extra day if you have time on either end of your trip. Guapi is a small Afro-Colombian town on the Guapi river, with a strong Pacific music culture — currulao and marimba are still performed at community gatherings. Fly back to Bogota or Medellin from Guapi's small airport rather than retracing the full journey.
The point of being on Gorgona is being on Gorgona. If you have limited days, spend them all on the island.