The island option, and its clock
The closest escape from the spit is by water. Isla Tortuga - actually two small islands, Alcatraz and Tolinga, off the tip of the Nicoya Peninsula - is about an hour and a half by boat from Puntarenas, with a white-sand beach, snorkelling and kayaks.
Watch the timing. Costa Rica's tourism board describes the ordinary day trips leaving from 7:30am, starting back at 4pm and reaching Puntarenas around 6pm, with no overnight stays allowed on the island. That schedule is built for land-based visitors, so on a ship day it only works on a tour that is timed to your all-aboard.
Busier ships, same pier
Puntarenas is getting more traffic, and it is coming as bigger ships rather than more of them. A September 2026 industry report put the 2025-26 season at 64 calls and about 90,000 passengers, with 72 calls and roughly 150,000 passengers projected for 2026-27. The season is concentrated in October to April, and the same report flagged ground transport and excursion staging as pressure points on multi-ship days.
Puerto Caldera, the nearby cargo port, is increasingly used for embarkation and turnarounds, so check which of the two your ship actually uses.
Sources: visitcostarica.com, thetraveler.org