Here are a few tips for Ireland based on our trip there in May. Since you've already been in Southwestern Ireland, you have probably already been in Dublin, and that's a place that's worth a few days to visit old haunts or try something new. We stayed at the Ariel House in Ballsbridge, which is a block from the Landsdown Road DART station. The Ariel has a four-star breakfast and is relatively inexpensive. Highly rated on TripAdvisor. You can walk to town or take the DART from Landsdown place.
We saw a magnificent play at the Gaiety, had a good tour at Trinity College, tea and cakes at Bewleys, and on and on. We walked everywhere and had a magnificent time. May will be just fine, but bring an umbrella whenever you go out.
There's a very fast, very cheap train to Galway. We reserved in advance. Galway is worth a night or two, and doesn't have quite the size and variety of Dublin. You can also head to the southeast on the DART to Greystones and then transfer to other train lines if you'd like to go to Wexford, for example.
Have a great trip.