Every year Llangollen hosts an International Eisteddfod where people from all over the world take part in musical and dancing competitions. (http://www.international-...)
The Llangollen Steam Railway (http://llangollenrail.lla...) departs from the station in the town. You can enjoy a 3-course meal on the train or just go for the ride.
Horse-drawn canal boats are available 50 meters from the town center at weekends and during the summer. Make sure you sit on the right side of the boat and then you'll be able to look over the side and down a 100ft drop as you pass over the Pontcysyllte aqueduct!
The fast flowing and rocky River Dee is popular with canoeists. You'll have to bring your own canoe though.