Just north of the heart of Dublin are two great getaways quite unlike the city center: Howth and Malahide. Howth is a quaint fishing village popular among tourists and locals alike for its quiet nature and stunning lighthouses. It's a great place to go in order to slow down, enjoy a walk, a tea or coffee, and a nice view. There are two lighthouses people go to see in Howth. There is Howth lighthouse on the north side and Baily Lighthouse on the south side.
To visit Howth lighthouse you can simply take an easy stroll down the pier and enjoy the views in all directions. From here, for €15 you can also venture out to Ireland's Eye via boat to enjoy the ultra relaxing bird sanctuary island. Like the birds, you won't be disturbed by a single car or even a bike.
For something a bit more involved you can take the coastal trail around to the Baily Lighthouse. While on the path you'll get great views of the Wicklow coastline and Dublin Bay. Unfortunately, if the weather's stormy, it's not recommended to take the coastal trail as it's pretty exposed in areas. In this case, just walk around the town of Howth and enjoy the slightly more protected coastline by Howth lighthouse.
Here's a fun map of the places you can and should explore in Howth.
Before or after enjoying this town, a great additional stop north of Dublin is Malahide. In Malahide there's a village, there are gardens, and most famously, there is the Malahide castle. This castle was built in the 12th century and was occupied and owned by the Talbot family for 800 years. The exterior is stunning and if you want to cough up the €12 (€8 for students), you can also have a tour of the inside as well as access to the botanical gardens (9:30-5:30 daily). If you're not looking to spend a lot of money, exploring the castle and gardens from the outside is still worth the trip.
If you're looking for a snack or a little shopping, just past the castle is Avoca Cafe & Shop which is best described as a cross between Anthropology, Urban Outfitters, and Whole Foods. Think Anthro style and pricing with the addition of quirky gifts and delicious food items (both packaged and fresh). I recommend at minimum getting a snack or a beverage and relaxing in the cafe overlooking the neighboring gardens.
Getting to Howth and Malahide: From Dublin City Center you can take the DART to Malahide or Howth for under €5 in about 30 minutes. There are two separate trains that run to the two final destinations, so make sure you hop on the correct one. The best way to hit both towns in one day using public transportation is to head to Howth, then back to Howth Junction Station and from there switch trains to Malahide North.