The National Cycle Network in North Wales runs south from Chester to Wrexham and then heads west towards Llangollen, Corwen and Bala to pick up Lon Mawddach at Dolgallau.
A section of the route is between Trevor and Llantysilio via Llangollen alongside the Llangollen Canal, taking in magnificent views of the Dee Valley and Castle Dinas Bran.
More details here: www.sustrans.org.uk/ncn/map/route/route-85
For bike hire in Llangollen, visit Cycles2go. They offer good deals on family bike hire, ideal for cycling along the canal tow path to Sir Thomas Telford's Aqueduct and beyond. They will even bring the bikes to the hostel for you and pick them up at the end of the day.