Whilst many attractions might offer limited hours , or be closed, entirely, there are still many MORE places worth visiting (at ANY time of the year) that make a winter visit worthwhile.
Before making any suggestions, though -- some questions:
Is this a First visit? What about Ireland peeks your interest -- scenery, culture, historic sites, specific locations? How long a trip? Where would you be flying in to -- and out of? Number of travelers? Self-drive (rental car), or public Transport? What's your Budget?
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Bob
Help Us to Help You. The more you tell us about your plans (dates, interests, budget), the better we can tailor our advice to suit!