Both cities are full of great eateries. So don't worry.
I don't live in either city but have eaten at
Milanos Oliver Plunkett Street, Cork.
Granted it's Italian food not Irish
There's a nice place beside Galway Crystal (sorry cant remember the name)
The food is good for a day not sure if it would be a 'night-out' type of place.
Oh if you fancy a drive then I love
The Lady Gregory Hotel
Ennis Road,
Gort,
Again I have only eaten there during the day.
It's a good place to stop if you are going to the Burren or The Cliffs of Moher
Also on the route to Cork - I think.
What do you consider Irish food? your not really going to get Bacon & cabbage many places LOL
Look up
http://www.toptable.com/en-gb/location/content/?l=3368
Go to one of the better hotels for a meal - they usually offer a wide 'Irishy' type range.
Might even get some cabbage ;)
Have a great trip
Hope the weather improves
Enjoy the 'Craic'