As an engineer I found the Llechwedd slate quarry museums very interesting. http://www.llechwedd-slate-caverns.co.uk/
Then there are all those lovely castles, Caernarvon, Beaumaris, Conway.
The Menai Straits suspension bridge.
The narow gauge railways. http://en.wikipedia.org/wiki/North_Wales_Narrow_Gauge_Railways
Have fun!