I would like to become a Spanish citizen. I was born and live in New York, my parents were born in Puerto Rico. My dad's parents were born in Puerto Rico before the Spanish American war, so they were Spanish citizens at birth or until the U.S. granted citizenship to Puerto Ricans and my mother's parents were born before U.S. citizenship was granted - 1900. Can I request Spanish citizenship? If yes, can I apply while living here?

Exiles’ children and grandchildren can apply for Spanish nationality since today...
Check out this link to find the answer to your question: La Moncloa. Exiles' children and grandchildren can apply for Spanish nationality since today (http://www.la-moncloa.es/IDIOMAS/9/ActualidadHome/29122008_MemoriaHist%C3%B3rica_Nacionalizaciones.h tm)

Hope you'll find the answer to your specific situation. Good Luck!:)