The largest coral reef is on the Caribbean side between Cahuita and Manzanillo (Puerto Viejo in between). Caribbean has a rasta flair, little infrastructure, is pristine and unspoiled. Aquamor is the best group to work with here.
http://greencoast.com/aquamor2.htm
In the central Pacific some diving is available around Manuel Antonio park but the real jem is south of Dominical at Playa Uvita and Ballena National park. This area has the second largest coral reef in the country is home to whales and dolphins and provides day trips to Canos to the south for diving in the wild southern Pacific.
Island diving in the northwest Pacific (Nicoya peninsula) is very popular with Bill Beard and many other capable companies. This is the driest area of the country and is a good choice from April-November (green season - plenty of rain in Central but especially southern Pacific).
Southern Pacific is the wildest part of Costa Rica where you will find Corcovado National Park, and the best diving spot Canos Island. This area is great during dry season (Dec-Mar) and has more sharks than anywhere else in the country.
For a map of national parks :
http://www.fun-costa-rica-vacations.com/costa-rica-national-parks.html
For a beach map showing Nicoya peninsula and Canos Island :
http://fun-costa-rica-vacations.com/costa-rica-beach-map.html
The northwest Pacific is the most tourist oriented area with Arenal, Monteverde, Rincon de la Vieja and plenty of American and European expatriates with hotels, bars, and restaurants. The southern part of Nicoya is less commercialized and more fun to me.