Congratulations! Since you are moving from the States, I would try to stay in a more tourist prone area. Fajardo would be a nice place that would have some decent neighborhoods to consider. Here is a link to a home for $950 in Fajardo,
Alquiler Bienes Raices Urb Terrazas Demajagua II en Fajardo Puerto Rico. You will find other beautiful, affordable neighborhoods to consider throughout Puerto Rico. Always aim for neighborhoods with either control access with a guard or without. It's a small island and unfortunately, everyone living in close proximity with each other, leads to issues. The location can make a huge difference.
Good luck and God bless!