Yes, an ATM attached to an actual bank, preferably when it's open so someone can help you if it eats your card or something. And use a debit card, not a credit card, to avoid interest charges.
In Belfast, try not to get more pounds than you think you'll need. They'll be Bank of Ireland notes, which may not be as readily accepted in the rest of the UK (though they could be exchanged at a bank). So you may not want to have too much left over.
I didn't find any reluctance in Kinsale or Dingle to accept cash or my credit card. Do what works for you. I try to use cash for smaller purchases and the card for dinners or bigger expenses.