While surfing alone is frowned upon for safety reasons, there is something to be said for the solace of just you and the water. Costa Rica is generally overrun with tourists, but with a little legwork, you can find a spot to surf that won't require you to be cheek to jowl with your fellow wave enthusiasts.
Matapalo, in the south region of the Pacific side, is one such place. The surf isn't always consistent, but it does have three point breaks that can be terrific in the right conditions. But remote is not an exaggeration; there are no restaurants, so the few hotels are all-inclusive. Nightlife is pretty much nonexistent. If you're truly looking for remote, Matapalo is your place.
Pavones, on the southernmost Pacific side, will also provide the quiet-seeking surfer a place to be alone. But at a price: It's not easy to get to (4WD might be a good bet) and like Matapalo, the services are limited. Also like Matapalo, the swell can be extremely rewarding -- and finicky. And always remember to be respectful of locals, who are less thrilled with eager tourists than their compatriots in busier spots.