Very early trip planning

I think 3 days in Dublin is probably enough especially since you'll probably have an extra day before you fly out. Belfast is probably best visited just after Dublin or just before you return to fly out. Most people will usually make a circular trip around the island one direction or the other but this is harder to do on public transport since it is more 'hub and spoke' from Dublin for main train lines and buses will probably be needed to fill in the gaps. Rick's book has a good overview of the trains and Ireland rail passes. You might really want to consider a train or train and bus pass once you have a preliminary schedule worked out. There's a briefer on-line version here: http://www.ricksteves.com/rail/ireland.cfm I personally think Galway is certainly the least interesting and least "Irish" of the towns you have listed. I would certainly work to see more of the Western coastal area than staying in Galway for multiple days. Much of Ireland is rural and while it can be slightly more difficult to get around rural areas without a car I think getting the feel for rural areas is important to understanding the country and the people. My $.02US, have a great trip!
=Tod

Thanks Tod, I have heard that about Galway from other places. Still trying to fine tune some things so I can work on places to stay.

We used Galway as a base and spent one day going to the Aran Island of Inishmore and another day driving around Connemara. We had a car but didn't use it the day we went to Inishmore. I know that there were also bus tours of Connemara.