I agree that Kinsale would be a great choice for an overnight stay before dropping your car at Cork airport . The little seaside town is beautiful and is a particular favorite here. It's popular with day trippers and tour companies so it does tend to get pretty crowded around midday, but arriving later in the afternoon would allow you to enjoy the place once everyone else has departed ... usually by 4 PM or thereabouts. There's a pretty seaside walk down to Charles Fort that's quite nice on a sunny day.
A potential stop along the way would be the aforementioned village of Cobh - pretty in its own right but which also has some historical significance in that it was the last stop for the Titanic before her date with the iceberg, and it was where the survivors and casualties from the Lusitania were taken after the ship was torpedoed off the Old Head of Kinsale in 1915. There's a little Titanic museum there that's worth a visit, and just outside is a statue memorializing the departure of little Annie Moore and her brothers who were the first inductees thru the newly opened Ellis Island in 1892. From Cobh you can take the charming little Passage West ferry to get to Kinsale.
We enjoyed the seaside village of Youghal, and there's a round tower and small monastic site in the village of Ardmore that you'll have pretty much all to yourselves.
If you don't mind meandering a little further afield the Rock of Cashel would be worth a stop as well.
I suppose departing from Shannon would be doable, but the sticking to the southern coast and leaving from Cork would be my suggestion.
BTW, it helps that the airport is south of the city and only a short drive from Kinsale. That way you needn't go into Cork city itself which frankly wasn't one of our favorites.
