Dublin
Old City

When the Vikings arrived in Dublin, they built a walled community along the River Liffey, in this area of Dublin. It was a busy town, filled with craftsman, merchants and traders, shops and market stalls, closely-packed houses, ships bringing goods from all over Europe. In the Middle Ages, the city expanded over the earlier Viking settlement.

Dublinia (next to Christ Church) - Dublinia is a hands-on history of Viking and medieval Dublin. Kids can step into a medieval fair - pass by the clothing stall (try on clothing and chain mail), pie stall, medicine tent, spices stall (guess the spice), scribe's stall (make a rubbing), play a drum or juggle. Also scenes from the plague in 1348, a merchant's house, busy wharf, plus a terrific model of Dublin in the Middle Ages.
In Viking Dublin, learn about Viking runes and life on a warship, sit around the fire in a Viking house, try on clothing, and walk down the streets of town.
At the end, you can climb up St. Michael's Tower, a solid stone tower with good views of Dublin all around (and continue on to Christ Church Cathedral).
Christ Church Cathedral - Christ Church Cathedral is the oldest building in Dublin, and the church interior glows with brilliant stained glass windows, medieval stone carvings and a colorful tiled floor.
At the entrance, pick up a copy of "A Young Person's Guide to Christ Church Cathedral" - things kids can look for in the church, such as the tomb of Strongbow (the great Norman lord who conquered Dublin), figures of wooden castles, the lion and the unicorn, the heart of a holy bishop.
Go down to the medieval crypt, where you can see stone pillars, original 13th century foundations of the church.
Dublin Castle - Dublin Castle is not what you might imagine, an 800 year old crumbling castle with birds roosting in the eaves. The castle is in tip-top shape, but it's not beloved by the Irish - when the English took over, they ruled Ireland from Dublin Castle.
To see the castle, it's a guided tour only in two parts. The first part is a tour of the state apartments and rooms (still in use), filled with crystal chandeliers, bright carpets and fancy furniture. Don't miss the presidents of Ireland heraldic coats of arms (each one gets to make up his or her own, if you like cats, you can have cats on your shield.)
The second half of the tour, the Undercroft, is fascinating. You go down inside the Powder Tower, built by the Normans on top of a Viking wall (which was cemented together with ox blood, hair and eggshells). Along with the Viking foundations, there's a Norman wall to the Poddle River and part of a bridge, bricked up in 1348 to keep the plague out of the castle (it didn't keep the plague out).
Dubh Linn Gardens - Adjoining the castle is a wide grassy area with park benches, the Dubh Linn Gardens. When you're standing in the gardens, you're walking over the site of the "black pool," the Dubh Linn.
St. Patrick's Cathedral - The national cathedral of Ireland, St. Patrick's Cathedral, is built on the site of a well where St. Patrick baptized Christian converts in the 5th century. All kinds of people are buried in the cathedral - Jonathan Swift (author of Gulliver's Travels), recent presidents of Ireland, soldiers, archbishops, notable men and women. Don't miss the Celtic grave slabs, ornamented with stone crosses and in the south transept there are two memorable statues of St. Patrick.
The green park next to the cathedral has a small playground with swings and slides for toddlers. (St. Patrick's well was located in this park, and there's always been a church at this site, although the existing cathedral was rebuilt in the 13th century.)