Hi NickW,
I remember the last time I was in Santo Domingo, that I saw a place in Bella Vista called "Samanel training center" something like that, in Avenida Bolivar, where I believe they offer computer classes. I know Samanel is a computer store, but the name "training center" comes to my memory.
Also, I know of a very popular computer school called "Escuela Nacional de Inform?tica", but that is not in Bella Vista, but in Gazcue, in Avenida Independencia, before the "Parque Independencia". I don't know specifically what computer courses are taught there, but you can check them out. Good luck.