My recommendation is to have a read of this post, and then use the Accommodation in Ireland and Getting Around Ireland posts to figure out where to stay.
Dublin Postcodes:
Dublin is divided into postcodes as you can see in this image (thanks to Wikipedia).
Other than the fact that the odd numbers are on the north side, and the even numbers are on the south they (in my opinion) really have no significance.
Dublin 1 and 2 are considered the inner city or city centre.
Generally, in terms of rent prices (with exceptions) the south of the city is more expensive (particularly 2, 4, 6 and 6w). Incidentally, the story of 6w is an interesting tale of an Irish solution to an Irish problem.
As a guide, anywhere that says "Co. Dublin" or "County Dublin" usually means that it is outside the city. Some places are further than others.
Like all large metropolitan cities, rent is very expensive in the city centre, and a lot of the population commute to and from work on a daily basis. Dublin is no exception.
Ideally, if you can, seek to rent somewhere close to where you will be working, however, if your budget won’t allow that, you can try and get somewhere else and commute.