Hi Megan,
Thanks for reaching out.
The tourism season generally begins in April, with longer days coming in and warmer temperatures, though still chilly with average temperatures of about 13C. If you want to experience the warmer weather, mid-late May is a good time, and still not peak tourist season, so you can get the best of both worlds.
In terms of your itinerary, I would recommend checking out these
Trip Ideas for some inspiration.
Let me know if you have any other questions and I would be glad to help out.
Cathaoir