As you approach the town you'll see the Pontcysyllte aqueduct (http://en.wikipedia.org/w...) carrying the Ellesmere Canal over the River Dee, its over a 100 feet high and a 1000 long. The aqueduct is quite an impressive sight, especially when you consider that it was built over 200 years ago.
There is a ruined castle, Dinas Bran, just outside the town. It is an open site i.e. no admission charge, and the view is worth the long walk/climb. Just behind the main stretch, on the other side of the canal, is the beginning of the walking path leading up, perpendicular to the canal. There are signs for Offa's Dike, though this too leads to the castle.
Visit Plas Newydd a half-timbered black and white house in its own grounds. The inside has been intricately carved and looks surreal to say the least!