I'd do the latter, spend the day in Kenmare. I love Cork city itself, but there's not an whole hell of a lot to see, and if the weather is nice, Kenmare is much nicer. Then stay at 1 of the 2 airport hotels and you're all set for the morning.

BTW, you said Kinsale in your first post. Kenmare is a lot further away from Cork airport than Kinsale...