Hi Cristine,
How exciting that you're going on your dream journey to Ireland!
First of all, regarding accommodation. In May, the tourist season in Ireland is not yet in full swing, but it's definitely busier than during winter. You could wing it, but especially in more popular destinations you might be better off pre-booking. To get some inspiration, check this
accommodation page.
Now, onto the exciting part - your itinerary! You mentioned wanting to explore Ireland's Ancient East by heading South from Dublin.
For County Wicklow, Glendalough and some of the other stunning forest walks are a must-do. You could even do a part of the
Wicklow Way. From Wicklow, you could go to Kilkenny. Kilkenny is a lovely town that would put you pretty central, so definitely a great suggestion for booking a stay. From Kilkenny it's also easy to visit
Rock of Cashel.
If you prefer to go more South from Wicklow instead, you could pay a visit to County Wexford instead. Stradbally is a lovely village to stay in, and from there you could explore Hook Lighthouse.
Two other cute villages/towns in the South where there's lots to do are
Kinsale and Cobh in County Cork. From there you could explore the Malin Head or the Ring of Beara.
I hope this helps you get started!
Let me know if you have any other questions.
Le Grá,
Alinde