A few other threads covering where to eat in Cork.
Can certainly agree with the suggestions for Greenes (they offer an early bird special between 5 and 6 [I believe, been a while since I went so time could be off] but that might be midweek only). In a very handy location from Tivoli (Silversprings Hotel), located at the Tivoli end of MacCurtain St.
Currans (down beside the gate cinema - full directions given by me on another thread) is also a good spot for some food with a nice atmosphere.
As for shows, not sure what's on in the Everyman at the minute, but usually something of note on (located across the road from Greenes away from the hotel a little). I'm sure you'd find a listing for it somewhere online, if not you'd certainly find the number and could check with them directly. The Shelbourne, next door, is also a nice spot for a drink or two.
Again, no knowledge of what's currently happening in the Opera house, but if the show currently in the Everyman didn't suit, this could be worth checking too (again, if you can't find info online try giving them a call for details).
Apart from that not too many shows around. A few drinks in the fun and festivities of Cork is never a bad thing, but being a Saturday night could be a little busy around town. Nice bar on Oliver Plunkett St. called "The Ovens" where it won't be too crazy, as close as you'll get to a quiet pint on a Saturday.
[No connection with any of the pubs/restaurants mentioned]