Hi, we are heading to Edinburgh this July 2 for a graduation and thought we would add on 4-5 days in Ireland for a taste of the country. What would you suggest? I am thinking 1 night in Dublin, 2 nights in Galway and then heading back to Dublin. What would you suggest?
I would suggest you take a look at RS's itinerary advice, available here:
https://www.ricksteves.com/europe/ireland/itinerary
Similarly, the At-a-Glance section ranks the destinations and sights within a country.
Assuming you're flying over from Edinburgh, you should look at flying into the airport that is closest to your areas of interest. Could be Shannon or Kerry or whatever. Rather than fly back to Edinburgh to head home, consider flying home from Dublin (as there are more direct flights to US from Dublin than from Edinburgh).
If it were me and I had five days for a first visit, I would stay in Dublin the whole time and maybe do a day trip to Newgrange, Glendalough, Giant's Causeway or Belfast.
What are you wanting to achieve from this trip and why have you chosen Dublin and Galway. What are you wantingf to do/see in both places. Will you have a car or are you dependent on public transport?
With so few days I would also just stay in Dublin the entire time. You will see more if you aren’t spending time getting from one place to the next and then back again. There are many day trips you can take from Dublin that will allow you to see a lot of the countryside. Newgrange, Glendalough, Belfast and the Giant’s Causway, and even all the way to the Cliffs of Moher if you don’t mind a long day on a bus. Otherwise, I would try to go straight to Galway and spend the entire time there, but that is the more difficult location to fly home from.