Hi David,
What an amazing gift for your wife's retirement! I am so happy you are planning on visiting the area her ancestors were from, and love your I daughter's name. :) Are you doing any research into her roots? There is a helpful section on the Community dedicated to
Irish Family History.
The beginning of June is a lovely time of year for a visit, and travelling around by
public transportation is a great idea. You can easily combine it with day trips to other places in the area, and you can schedule and arrange those once you're here. Have you decided on what you'd like to see yet? Take a look
here for some suggestions for day trips from the city.
For an overview of recommended accommodation in the city, take a look on
this page. Are you looking for a hotel or a different type of accommodation?
From Cork City to Shannon Airport will take just under three hours by public transport, and Killarney is about three hours away. This of course also depends on if you're travelling on a Sunday when the bus schedules might be different. It is also an option to stay close to the airport the night before your flight, so you can easily make your way on the day of your flight home.
I hope this was helpful, and that other members will be able to provide you with their tips and recommendations as well! :)