Manuel Antonio Nat'l Park
Manuel Antonio National Park (Parque Nacional Manuel Antonio, in Quepos), one of Costa Rica's most popular parks, is quite easy to get to from San Jose. Right on the ocean, Manual Antonio is a dry-ish rain forest with mangroves and swimming beaches.
The trails through the park are easy, mostly level walking trails, and you can explore on your own. From the entrance, a good route to take is to walk along Playa Espadilla, swim at Playa Manuel Antonio (Manuel Antonio Beach), and walk back along Sendero El Perezoso.
At the entrance to the park, it's a good idea to hire a naturalist guide to help you see all the marvelous wildlife in the park. The guides have spotting scopes, and most importantly, know where to find all those beautifully camouflaged animals (we stood with an iguana practically right under our feet, and didn't see it until our guide pointed it out).
We saw common tent bats, tiny little proboscis bats, howler monkeys making lots of noise, a mother and baby three-toed sloth and a two-toed sloth snoozing in the trees, black iguanas (which are really black and ochre colored, and hard to spot on the rain forest floor), a basilisk iguana with a big fin down the back, toucans, iridescent hummingbirds, and squirrel monkeys. We spent some time just watching a (non-poisonous) golden silk spider hypnotically spinning a shimmering golden web.
Bring swim suits to swim at Manuel Antonio Beach - the beach is a sheltered cove with wide sandy beach, turquoise waters, plus picnic tables, bathrooms and showers to rinse off after your swim.
Because it's so popular, Manuel Antonio can get crowded. The high season is December/January to April. Late May or June is a good time to come, as it isn't all that crowded, and it's just the beginning of the rainy season (October is the rainiest month).
Tip: Manuel Antonio National Park is closed on Monday.