If you can stay 14 days, it's worth it.
A full week in Dublin is too long. Four days max is quite enough. Day 1: recover from jet lag and visit low-key sites near your hotel. Day 2: See a few of the big sites in Dublin City. Day 3: Take a full day coach tour of an attraction you'd like to see in the countryside near Dublin (the Visitor's Center can arrange something for you). Day 4: Partial day to sightsee/shop in Dublin and then get your transportation. With the other 3 days, I'd head to Northern Ireland (Belfast, Derry, Giant's Causeway/Antrim Coast).
While the train system is not extensive, it gets you to the major cities and the bus service fills in the gaps. In some areas, bus service is more frequent during peak tourist months. At any time of year, you can base in a lot of major cities and do private day tours via coach from there (i.e., Galway for Connemara, Aran Islands, The Burren, Cliffs of Mohrer).