I would suggest to stay in Santo Domingo, as few people said here, you can find many areas there where tourists won't go. We lived in Cabarete for 2 years (very small tourist town) and where we lived tourist didn't come, yet we had all the advantages of having power, water and internet
I dont know when you lived in Cabarete, but now its difficult to find a place where tourists dont come. Yes there are places where there are LESS tourists, but they really are everywhere...
I Understand what Matilda is saying though, you might be more comfortable in an area that is somewhat touristy, not only for the electricity and water and such, but also because some people like it to NOT speak spanish once in a while, or to NOT speak with a dominican (im not saying everyday, just once in a while). It's not only material stuff that you will miss, you will also have to get used to the culture, and while most of it is fun, some things are not and you may want to talk about it with someone that understands.. (other tourists)
That said, some people do fine in all dominican areas, but as 'a starter' you might be better off in a mixed area with tourist as a minority, when you are more used to life in the dr, you can always move to an all dominican area
By the way, I think just the city of Santo Domingo would be perfect, you basically have everything in one place.