If you're just coming for a couple of days, then you should be able to find things to do in Dublin. Not sure how much you're into museums, but I highly suggest Kilmainham Gaol. The Guinness Storehouse is also okay (it's better than Jameson Distillery). Trinity College offers a guided tour in conjunction to seeing the Book of Kells. Both are pretty interesting. Dublin has those hop on/hop off tour buses, which are a great way to see the Phoenix Park. Not sure what time of the year you're going to be there, but if you have time (and if it's open) Farmleigh, which is on the far side of the park, is totally worth a visit. I'm pretty sure the hop on/off bus goes up that way. Dublin has no shortage of pubs, so you should be okay there (I recommend the Stags Head and the Longstone). You can walk around St Stephen's Green and take a walk around the Georgian squares (Merrion and Fitzwilliam). If you're still short on things to do, you could take a day trip to the Wicklow Mountains, Malahide, or Newgrange.
As for shopping, the main areas are around Grafton Street and Henry Street. Both are city centre, they're just on opposite sides of the Liffey. If you wanted an American-style mall you could get the LUAS (the tram) to Dundrum Town Centre. It's worth the trip out if you're really into shopping. Avoca is good for Irish goods and the restaurant upstairs is pretty tasty.
Kilkenny, which is a total tourist shop, has a pretty great breakfast. Fallon & Byrne will have some American goods if you have room in your bag! They also have a restaurant, but I've never eaten there. The Porterhouse is our favorite place to drink (they have an awesome selection of Irish and international beers) and their food is pretty tasty. There are some good Chinese restaurants on Capel Street. I would NOT recommend going to The Church even though it looks cool and is very handy to Henry Street shopping. The drink is expensive and the food is not good. Oh, and of course there is Boojum where you'll find huge burritos and Dos Equis beer!
Hope that helps! Let me know if you have any specific questions! If you have time and I'm still here, I'd love to meet up for a pint!