Before I get to my point about ATM fees, here is some advice for newcomers. If you walk into and out of a bank on a main street and/or use a street ATM, there is a chance that a tigre will be surveilling you. If you do this, pause when you are ready to leave, scope your surroundings, and look back when you are walking to confirm that you are not being followed.
Once, when I entered and left Banco Popular on La Mella in Sto. Dom., my girlfriend, dominicana, who had been waiting outside, told me to get back inside. I was being surveilled. When he knew that we knew, he walked away. I got a physical description from my girlfriend, particularly color of shirt, so we could look out for him.
This is not paranoia but an intelligent security precaution so you can stay safe and happy in the D.R. It is better to use an ATM inside of a store, such as Plaza Lama or La Sirena. When you exit, no one knows that you had used a ATM inside. It is harder to be surveilled.
Now to my main point. Arbitrarily, I have been making ATM withdrawals from Banco Popular for ten years. Recently, the machine asked if I would accept the fee of RD$195.00. I clicked "yes" and completed the transaction. But when I looked at my receipt I found that the fee was actually RD$ 250.00! That's a lot of money! I complained to the manager about the deceit, intentional or not, and asked for a refund of 55 pesos. He refused on account of the Dominican more of refusing to refund any money under any circumstances, which is a whole topic in itself, and could take up an entire thread.
Solution? The solution I am looking at is obtaining a debit card and paying no more fees. The problem is that all banks require a host of difficult to obtain documents for foreigners. But if you plan to stay here for the rest of your life, like me, maybe the effort is worth it. If you go to a bank, just go to Services and ask for the document that lists account requirements for foreigners. I am now going to different banks to find out if some have requirements less onerous than others. "The jury is still out" on the answer to this question.
BTW, Banco Progreso has the lowest ATM fees I have found anywhere: RD$150.00. Also, the machines are beautifully designed. Many banks have machines whose buttons are slightly off center as they align with the text. You may press the wrong button. The Progreso machines do not have this failing. And "English" is clearly available to select.