Try these...
1. Volcan Arenal. Spectacularly amazing. A real life live volcano, with rumblings and mini eruptions most days and nights. Stay in a hotel in the village of El Castillo for incredible night time views of flowing lava. Then in the daytime, take a swim in a hot river (incredible! natural jacuzzi! leaves your skin so soft for days!), or go to the more official hot spring resort; and make sure you take a road trip around Lake Arenal for more breathtaking scenery.
2. Rio Celeste. In one of Costa Rica's many lush national parks is a river that is blue because of the minerals in it. I would suggest walking (or, if you are American, hiking) to the waterfalls and then further up to where you can see the river draw its colour from the earth.
3. Barra Honda. Caves hundreds of feet deep full of stalagmitey stalactitey stuff. Again in a national park bursting with flora and fauna.
4. Monteverde. One of the lushest of all the national parks, a good spot to do the zipwire through the jungle canopy, take a guided tour through the park to spot weird and wonderful creatures and plants (seriously, some trees are really interesting), and pop in to see some of the world's largest collections of insects and reptiles.
5. Near the border but in Panama - Bocas del Torro, especially Playa de Las Estrellas. The most picture perfect beach, deserted, except for hundreds of big starfish. Take a snorkel mask. Then you could go to red frog beach and scour the plants for the tiny weeny poison dart frog.
6. Caño Negro. Swamplands in the north. Billions of caymans and birds and stuff, seen by boat. Also if you want to see proper huge crocs, stop off at the bridge between San Jose and Jacó over the Rio Tarcoles and peer over. Dozens of 'em just waiting for the neighbouring farmers' cows to get thirsty.
6. Montezuma, where we live and have our business! For a list of reasons why THAT's amazing please see this page on our website:
http://casascolibri.homestead.com/About-Montezuma.html