Howth is a small town north-west of Dublin. It is located on a peninsula closing Dublin's bay.
You can reach Howth using the DART, a fast train service, from Dublin's city centre. Return ticket costs €3.40 from Connolly station and is valid one day. There are trains every 15 minutes. Take the train north to Howth. You will arrive near the Harbour. Notice: There is one train going to Howth, and the other going to Malahide. They both go in the same direction, but do not halt at the same stations. If it's not written "Howth", it's not going there.
Alternatively, you can take a bus from Connolly, line 31 will take you up to Howth's Harbour and line 31B up to Howth's Summit. Tickets can be bought in the bus (prepare your change). There is approximately one bus every half-hour or so. Do not trust timetables printed on bus stops.
Think walking shoes, as you'll mostly be walking. There is only one main (and circular) road on the peninsula, that bus lines 31 and 31B take.
The old town and the harbour are very traditional. There are interesting ruins higher in the hills, and an old tomb west of the harbour.
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 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.
It is also possible to go towards the centre 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.
There are a few restaurants on the peninsula, very "chic" and expensive for most of them.
There are a few pubs, too.
It is possible to go on a birdwatching cruise to Ireland's Eye, a small island north of Howth.