There is a walking trail starting east of the town that follows the cliffs all over to the southern part of the peninsula. Take the leftmost road from the harbour. The cliff's trail is indicated to the left a bit further. The view is breathtaking and it's really worth the walk. Along the way, you'll come across Dublin's most visible lighthouse, the Bailey Lighthouse open for tours once a year during the summertime Howth Peninsula Festival. The southern part gives a great view of Dublin's bay and the city itself. The whole tour takes between 3 and 4 hours.
If you took bus 31B to Howth's Summit, reach the lighthouse from there 15 minutes walk, and do half the track -- towards the north or the south. When you get off the bus, you will see The Summit Inn and a steep upward road beside it. Follow that road to the summit carpark at the top and from there you can choose Northleft or Southright. North will be busier but if you go South, you will be disorientated when you reach the end as it comes out about 10 minutes walk from a bus-stop. So north may work better.
It is also possible to go towards the center of the peninsula and walk to the three hills that dominate Dublin's view over the ocean. There is a golf course between two of the hills. The view is also very nice.