Ecuador is good for "environmental stuff" I suppose, with easy access to the rain forest on the east side of the Andes as well as attractions like the Galapagos Islands. But don't count on being warm there, if you're planning to base yourself in Quito. Due to its altitude, the climate there is cool and spring-like year-round. If you want warmth you could try Guayaquil but frankly, three months there would be 2.75 months too many. IMHO.

You seem interested in Chile as well and Santiago is a livable city all year round, but from May through August warm it's not.

Here's a suggestion: try Panama City. I have a cousin who spent three months there a few years ago, telecommuting as you plan to do. She really enjoyed it and whatever time of year you go, it's going to be warm. Also it's the hub of Copa Airlines which offers reasonable fares to practically anywhere in Latin America, so you can make plenty of short hop trips during your stay.