Some great suggestions here!
Cork English Market is great for having a stroll around and the produce is very good quality (especially the fish) if you fancy cooking something up. When the sun is shining take a walk to Fitzgerald Park and bring a picnic with you, you can set up your picnic by the river-side and perhaps get stuck into a book. There's also a free museum on the grounds of Fitzgerald Park, Cork Public Museum.
If you want to get out of the city for a bit then take the train to Cobh, not free but reasonably inexpensive (I think it's €8 return). In Cobh you can check out St. Colman's Cathedral, Cobh, you'll get great views of Cork Harbour from up there too.
When it comes to entertainment in the evenings, it's worth checking out upstairs at the The Oliver Plunkett, they usually have a decent traditional Irish gig going on and it's a bit more spacious then Sin é and An Spailpin Fanac (although the later two are a bit more authentically Irish). Entrance is free but you'd be expected to buy a drink if you want to stay there and enjoy the gig. If you want to buy yourself a stout, then the main Cork stouts are Murphys or Beamish (beware Beamish in particular is an acquired taste). You'll also be able to get Guiness on tap but Guiness is a Dublin stout and since your in Cork you might as well try the local stuff! :-)
Cork is a great, compact city - the locals think that it's the REAL capital of Ireland! It is small enough to walk around and is on the banks of the river Lee. Luckily there are plenty of cheap and even free things to do! Checkout Triskel Arts Centre Crawford Art Gallery and Collins Barracks museum Spend an hour or two wandering around The English Market - an old Cork institution. Breakfast at the Farmgate Café in the market. If you have a car or like cycling go to Kinsaleand have lunch in Fishy Fishy Café Go on a pub crawl - there's one called Cork Rebel pub crawl, reputed to be excellent. Cork has many lovely walking trails.
Here's a useful link:http://www.walkingroutes.ie/WalkingTrails/Cork
Don't miss Saint Fin Barre's Cathedral and the grounds of University College Cork are lovely. You can eat cheaply in Cork. Fish is particularly good. Lunch of soda bread with crabmeat or smoked salmon with a glass of Guinness can be had for less than $15. There is a very nice cafe in Crawford Art Gallery or pack a picnic from the English market, where you can buy the most wonderful food.The English market (a small part)
Have a great trip!
It's been years since I've been, but I loved the Ballycotton Cliff Walk-stunning. The The English Market is a lot of fun to wander around, grab some food for a picnic or find local crafts. St Patrick's St is the place to shop, grab a pint or just people watch.
Not far from the city of Cork, along the coast is a lovely little village, Kinsale. The Charles Fort is a lovely walk through. Give The Bulman Bar & Restaurant a try for excellent food, warm traditional atmosphere and lovely views.
Lastly, I'm a bit of a Titanic buff, so if you are intregued-you must visit Titanic Experience Cobh-it was the last stop before crossing the Atlanic.