There are a surprising number of English newspapers published in Costa Rica. Here is a list of the main ones, as well as the major national newspapers published in Spanish.

English Newspapers:

The Tico Times
http://www.ticotimes.net/
Published Weekly

AM Costa Rica
http://www.amcostarica.com/
Online daily news, no print edition.

Where In Costa Rica
http://www.whereincostarica.com/
Online directory of local events.

Inside Costa Rica
http://insidecostarica.com/
Local news in English.

The Beach Times
http://www.thebeachtimes.com/
Distributed on the Gold Coast, focus on local news.

The Guanacaste Journal
http://www.journalcr.com/
Distributed in Guanacaste only, focus on local news.

Spanish Newspapers:

La Nacion
http://www.nacion.com/
The most widely read national newspaper in Costa Rica.

Al Día
http://www.aldia.co.cr
Popular national tabloid.

La Republica
http://www.larepublica.net
National Business news.