There is a place on the main street in Sosua that sells the Miami Herald. No more than one day old. Right now he seems to have only one copy, but would provide for you, i'm sure, if you wanted it on a daily basis.
But why do you want newspapers? All the big newspapers and news magazines have websites and you can get alll the latest news from them.
In Sosua there are a number of internet cafes. Don't know what the present charge is, but cheap. I'd guess about RD$50/hour. I don't think any of the AIs in Sosua have internet cafes; too much local competition. Tell me what hotel you will be staying at and I'll tell you the closest internet cafe(s).
Yea, we have a regular relationship - he tells me how bad his life is 'cause I don't buy his newspapers and I tell him how bad the news is that he is trying to sell. Quite a sweet guy and regular as clockwork.