The Irish generally have not overly spoiled most of their tourist attractions, but there is one attraction in Dublin that is slightly on the cheesy side and yet informational and interesting: Dublinia!, which highlights Dublin's medieval beginnings.
Dublinia is located in a historical building connected to Christ Church via a pedestrian bridge. When entering Dublinia, you can in fact choose to purchase a double ticket for Dublinia/Christ Church. Admission for just Dublinia is €4, with family passes available for €10. If you're interested in seeing both, it's not so much a bargain as a convenience, because after seeing Dublinia and crossing over to the church, you can pay for a church ticket there if you change your mind.
On your way into the building, have fun posing in the painted boards that make you look like you are a medieval knight or lady. Once you enter, Dublinia starts out with an exhibit which focuses on the medieval history of Dublin: how it was founded and primarily how its markets evolved. This is a pretty good place to take kids, as Dublinia encourages "hands on" exhibits and lots of how-and-why-type explanations for the exhibits. You learn about the various plagues that have hit Dublin (the "Plague and pestilence" sign is almost cheerful) and about some of the early leaders of the city. While Dublinia does not progress much beyond the 1800's, it is an entertaining (if occasionally bordering on cheesy) look into the history of Dublin.
Those with children or those with an interest in history will find Dublinia an interesting glimpse into Dublin's past, but I would not rate it on the 'must-sees' of the city if your time is limited here. Even if you do not go to the actual exhibits, you can enter their gift shop via the Christ Church side entrance, and their gift shop is one of the more interesting ones I saw while in Dublin.