You have a lot of places to choose from Alison. :) As Railtours Ireland
already mentioned, there are options to explore the west coast from Dublin by rail where you get to see Galway and the Cliffs of Moher. You can also pick between one of the many coach tours
that leave from the capital. Maybe a multiple day tour is an option? This way you'll have more time to see everything you would like to see.
It's really easy to explore the Causeway Coastal route and Northern Ireland by coach from Belfast, so it's a good place to use as a base. Take a look at the options here
Getting around Dublin is easy, and you've got several types of transportation to choose from. Depending on where you would like to go you can hop on a bus, DART, or Luas, and you can use this handy Journey Planner
to plan your whole trip. My advice is to make a list of the things you wouldn't want to miss and see how many days you would need to visit them all. The Dublin Pass
is a time saver because it's a ticket to 33 popular attractions in Dublin, and you won't have to stand in line. :D
On our website you will also find all of the different ferry companies
that go from Ireland to Wales and back.
I hope this makes the planning of your trip a wee bit easier, and just give me a shout if you'd like to know more!