I'm quoting a post I made before because I'm too lazy to type a new one;
I live in Dublin so pm me if you have any questions.
Most of the museums are free, the best one is michael collins baracks, alot of school trips leave it out for some reason and the natural history museum.
Don't shop on grafton street-too expensive. Henry st is the shopping street, it's the street across from the spike (don't worry you'll know the spike when you see it
Georges arcade market is worth a look, on george st near the Olympia theatre.
You'll need correct change to ride the buses and you don't get change back so it's a good idea to get a rambler card (most newsagents sell them).
Get a hot chocolate from butler's cafe, there's one next to the spike.
When you're going through the arch in trinity college, please don't block it. Students have to use it too.
There's alot of places to eat in temple bar- don't be tempted to go into the 'orish' pubs for food, they'll fleece you. But if you must... I've heard good things about The Boxty House (21 Temple Bar) even if it is a tourist trap. Here's a list of nice places to eat. I know you're only staying in Dublin for a couple of days but I don't know what type of food you like so you can pick
Burger: The Counter (Near pizza hut 20 Suffolk Street and Dundrum),Gourmet Burger Kitchen (5 South Anne Street)
Sandwiches: Munchies, Cafe Irie (11 Fownes street)
Normal: Fallon & Byrnes (17 Exchequer Street)
Fancy: Chapter one (18 Parnell Square North), Restaurant Patrick Guilbaud (21 Upper Merrion Street)
Pizza: Gotham cafe (Anne st)
Chicken: Crackbird (34 South William Street)
Breakfast: Honest to Goodness (Georges Arcade)
Brunch Odessa (13-14 Dames court)
Italain: Carluccios (52 Dawson Street), Toscan (Dame Street(opposite Dublin Castle)), Steps of Rome
French: Green hen (Exchequer st), Chez Max (next to Dublin castle), L’Gueleton (1 Fade St off georges st), La Cave (28 South Anne Street),
Tapas: Salamanca (Dame st & St Andrews st)
Japanese: Yamamori (71-72 south great georges st)
Dim sum: Good World chinese restaurant (18 south great georges st)
Chinese: Manna Chinese Restaurant (Parnell st),
Chinese and Korean: Hilan (45 Capel St)
Noddles: Wagamana, Diep Noddle bar (Mortons, Hatch st)
Thai: Koh (Millieium centre)
Cajun/Creole: Zante Zoe (Crow st)
Persian: Zaytoon (Parliament st)
Greek: Corfu (Parliament st), Steps of Rome (1 Chatham St)
Moroccan: DaDa (45 South William Street)
Crepes: Fafie’s Creperie (Kevin St)
Milkshake: Shakes (15 College Green)
Sunday Roast: The Exchequer (3-5 Exchequer Street)
Vegetarian: Cafe Fresh (Powerscourt)
Dublin is a bit like new york, don't stop in the middle of the street when it's busy.
American tourist stick out like a sore thumb because they generally talk fairly loud and as such are a favourite target for pickpockets. Of course not all American's talk loud but the Irish are more reserved. Also Dublin city is very centralised, nearly everything is within walking distance. It's not a good idea to take out a map in the middle of the street, look at one before you leave but if you get lost just ask for directions.
The viking river tour is meant to be good but I haven't done it so i'm not sure on that one.
Don't attempt an Irish accent that sounds like the leprechaun from the lucky charms ad, you're likely to be slapped.
Irish alcohol has a higher percentage than in America, so even if you see something you recognise like bud keep in mind it's not the same percentage.
Thats all I can think of for the moment.
Edit: knew I forgot something, tipping is optional. you only tip for good service and only really in restaurants and cafe's. it's generally 10%, 15% for someone who really went above and beyond.
The trend is here if you want to take a look at it http://www.etiquettehell.com/smf/index.php?topic=76489.msg1798580#msg1798580
I know nothing about Cork as I have never been but I 'think' there's a toll bridge on the motorway so remember to bring change.