You don't have to worry about wasting any time on day one looking for an ATM. They have one at every airport. Also, there are cambios at every airport. You may not get the best exchange rate there, but just exchange $100 or so - enough to get you through day one.
I would advice against using just any ATM. The most secure ones are those attached to a bank, and better yet - a major bank. I would avoid any hasty locations.
For the exchange rate, I would also advice against exchanging on airport, any agency back in your home country should have significantly better rates than any agency at an airport. So change a bit before departing, then use casa de cambio in the DR, but not at the airport. It might be just for one day, but you can lose a nice amount of money anyway.
I was once out of USD when entering and had to buy the tourist card, the exchange rate of USD/EUR was actually 1:1. And this wasn't now, it was when the difference was actually big. I know the rate USD/DOP might pretty much always be better, but still, I would not do it.