Aberystwyth
Aberystwyth Castle stands open to the sea breezes. An especially ruined ruin, this was once one of Edward I's eight "iron ring of castles," built to subdue those rebellious Welsh. Don't worry about the condition of the castle, there's a fine park for kids to run around.
At the other end of the bay is Constitution Hill. To get to the summit of the Hill, take the Cliff Railway, a Victorian tour de force and the longest cliff railway in Britain. Fabulous views of Cardigan Bay from the top.
In the center of Aberstwyth, stop in at the Ceredigion Museum, a folk life museum, with a cottage from 1850, and displays of spinning and weaving, mining, agriculture, all located in a restored Edwardian theater.
From the train station in town, take a spin on the Vale of Rheidol Railway. Ride on this steam train from Abserystwth up the Rheidol Valley to Devil's Bridge. Devil's Bridge is three bridges, the first built in the 12th century. From Devil's Bridge there are a number of walks in the woodlands, to Mynach Falls and the Devil's Punchbowl.