Wicklow Mountains National Park ~ Ireland
Wicklow Mountains National Park is the closest National Park to Dublin. So if you're trip only includes a few days in Dublin, I would absolutely recommend taking a day trip excursion out of the city and into this beautiful landscape. It will at least give you a taste of what the rest of Ireland has to offer and it is only about an hour south of Dublin. There are many tour companies that offer day trips (check TripAdvisor for some good options).
However, the much better alternative is if you're driving yourself from Dublin through the rest of the country - then you have way more time to stop & savor every bit of Ireland at your own pace. Just drive around and stop whenever you see something that catches your eye (which will likely happen often).
**See my full Ireland itinerary here.