Hi Julia, 

Costa Rica is Le Costa Rica in French and it is masculine so you will say 

I wrongly believed that C R was an island and would have said à but on research, it is definitely masculine and not an island.

Take a look at this tourism page - Quand partir au Costa Rica :

https://www.costarica-surmesure.com/conseils-voyage/quand-partir#:~:text=La%20p%C3%A9riode%20id%C3%A9ale%20et%20recommand%C3%A9e,se%20soucier%20de%20la%20m%C3%A9t%C3%A9o.

 

Bonne Continuation !