The natural day trip is Cahuita, half an hour up the coast, where the national park has a beautiful coastal hiking trail and one of Costa Rica's only living coral reefs. The Aviarios Sloth Sanctuary on the way is a worthwhile stop.
In the other direction, hop a dugout up to the Bribri village of Yorkin on the Panamanian border for a day with the Stibrawpa women's cooperative. The town of Bribri itself is worth a look for the busy Saturday market and a hint of the indigenous Talamanca canton beyond the tourist coast. Across the border, the islands of Bocas del Toro in Panama are a day trip if you want a passport stamp but really deserve at least an overnight.