I can highly recommend
Wynn's Hotel on Abby Street, just of O'Connell St. We spent 10 days there during the summer and really enjoyed it.
It is old fashioned in a nice way and the staff really go out of their way to help you. The food was excellent, although the restraunt is not open each evening, however the bar food is available every evening. The bar is very popular in the evenings, but the patrons, mainly from the country, are friendly and very talkative.
The location is excellent, trains, trams and busses are all within easy access and in less than a minutes walk you are on O'Connell St., where you can join bus tours etc.
As with any city center hotel, you can expect to hear the sounds of the city and there is usually some kind of party in the ballroom on the second floor on Saturday nights. But it really did not bother any of us (4 adults).
The standard rooms are a bit on the small side for a long stay, so I would recommend a deluxe room, if the budget stretches to it.
Oh and on a techie note, the Wifi was excellent and available in all the rooms.