In terms of gay CR, the Pacific coast town of Manuel Antonio is as gay as it gets. There is a small but significant ex-pat gay presence there, and even a gay beach walking northward up the coast from the principal beach.
The nature is impressive as well. The jungle, especially inside Manuel Antonio's national reserve, literally runs right into the ocean. You can sit on the beach and share it with monkeys and the occasional reptile.
Other sites that could be 'must-see,' depending on your interests, include:
*Zipline tours in Quepos (traditional rainforest) or Monteverde (cloud forest)
*Endangered turtle watching in Tortuguero (in the Caribbean province, Limón)
*The beaches in the northwestern province of Guanacaste
There are also volcano tours of Arenal and Poás, but IMO they aren't worth the effort, especially in November (which is still the seemingly NEVER-ENDING rainy season). Others may be of different opinions.
Other than Manuel Antonio, San José is the main (perhaps only?) other center of gay life. There are several gay bars -- Avispa (Wasp) and Puchos come to mind but I'm sure there are others. There are also gay accommodations in San José that are relatively economical, as well as at least two bathhouses (one's called Hispalis), but I can't provide any insight into how they are