In the 1990's I backpacked through the natural areas of North, Central and South America. During that time, I spent a month in Costa Rica. As this was almost 20 years ago (!), I can only write generally about the nature and wlldlife options there.
Costa Rica is a small country in central America, located between Nicaragua (to the north) and Panama (to the south). Its name means 'rich coast' and indeed one side of the country has the Caribbean (in the Atlantic Ocean), the other faces the Pacific. It often tops list as one of the 'greenest' countries in the world. Amazingly for a country in Latin America, it abolished its military in 1949.
This is a fantastic country to explore neotropical rainforest. It is relatively safe (no military!). Due to the influence of the USA, English is widely spoken. And they have a great national park system. National park entry fees and permits, and tours, etc are more expensive than in most other parts of South & Central America, but they are usually worth it.
The great thing about Costa Rica is its range of habitats and associated wildlife in such a small area. They have an amazing range of ecosystems within a small country, from highland to lowland rainforest, from dry monsoon forest to coral reefs. The corresponding animals and plants in this range of ecosystems is so high that Costa Rica is often said to have the highest diversity per area of any country in the world (although this is a hard claim to prove). Another factor in this diversity is the fact that it is situated in Central America and thus the plants and animals are a mix of Nearctic (from North America) and Neotropical (from South America).
Corcovado National Park is located in the south west. It is the largest national park. When I visited there over a decade and a half ago, it required hiking in a fair way to get access to a fairly basic research station. I understand this is still the case. This is great, as it really means the area is unspoiled. During the day I saw tent-making bats under leaves and agouti/paca and peccary on the forest floor, and toucans in the canopy. At night I spotlighted tapir.
In the north-west is Santa Rosa National Park. This park is 'dry' rainforest, or savanna, with trees such as thorny Acacias. Here I have sees a mixture of neotropical (South American) animals (such as army ants), and Nearctic (North American) animals (skunk, white-tailed deer, etc)