What I am going to write here is NOT a recommendation!
There are safe enough barrios which I deem survivable by (some, even many) foreigners. Now, we need to re-define what qualifies as a barrio for us or Dominicans or both (if that's possible). Some Dominicans consider La Union (a Balaguer area social housing complex opposite to POP Int'l, Sosua) a barrio (I think it's way better that what I call a barrio, however). I know of at least two foreigners living there. Rents start at RD$ 2000.oo (USD 60.oo) a month. There is occasional water (unless you have or can install a water reservoir on the roof, locally called a "Tinaco") and electricity comes in for a couple of hours during the DAY (pun intended!). Security is limited to the true friendships the resident is capable of making among his neighbors an ability to stay out of stupid trouble. I am able to observe one foreigner living in the midst of all this and I am amazed at how well he is doing, even though his linguistic skills are limited and he still is not quite used to all the crowdiness and noise and has hooked up with the all around wrong girl (IMHO), and he's doing it all on more or the budget in question.
This is just one example, and I am sure there are more place like these where one can live a low cost but quite "Dominican" life even with limited experience. BUT as I stated above, it's not a recommendation and not all social housing developments and/or barrios are the same... even if they can look very similar at first glance.
Also as for the simple or "Dominican" life... there is not just barrios and batteys. There is also "el campo", the country side. I've stayed several times in campo locations and felt safer than anywhere else (and I live in a very safe place). Most of all I was more than well received. Values are still much more traditional... less if not no tigueres at all... people helping each other. Casita de tablitas de cololes (wooden shot gun shack) on a little land to raise your goats, pig and chicken and plant some yuka = RD$ 2000.oo or less a month or own for a few grands (less than 10... US, that is). People will help you along and look after you and if you grow old and get seriously ill... they will feed you some stuff with strange tastes and it may actually cure you... and if not, they will mourn you for 9 days, not just because you where the richest guy in the hood with your 900 Dolare cada lo trenta dia, but because you lived AMONG them.
But the "Stranded On A Caribbean Island's Beach"-dream-lifestyle, is something nowadays only a few very privileged people seem to be able to afford successfully and safely.
... J-D.