Generally first-time visitors to Ireland want to hit the high tourist spots with some charm thrown in on the side. Most castle hotels are pricey but Tony's suggestion of Ballyseede is one of the lower priced ones. It is not too far from Killarney toward Tralee. Some small towns that I consider charming would be Kenmare, Adare, Dingle, Kinsale, Cobh. Some of those can be "touristy" on weekends especially Dingle and Kinsale.

To speed up getting to Dublin Airport in the early morning from the city pre-order a taxi the night before. It might cost a little more than the bus but it will make it quicker and easier.