I do not know what these places are called, but you get them everywhere in the DR, I see no reason why where you are should be different. You drive into a garage, the garage has a little room with bathroom attached. You pay some guy 500pesos and no body bothers you for the time you are there.
I have dropped a friend off in one that stank of wacky backy but I reckon in DR these are prostitute places also, but I suppose you can can stay there alone.
I've come across them in Africa before and they are good cheap head down places to stay. All you need if you want to get sleep.