From Rhyd-y-Bryn why not leave your car and gain access to the many woodland walks directly from the gardens. This part of Wales has excellent walks to suit all abilities from a ramble to the famous Loggerheads country park to the more exertive climb to the top of Moel Fammau. There are many good local hostelries offering good beers, wines and food including the old Miners Arms in the village.
Further afield the Snowdonia National Park is easily accessible with its mountains and rivers.
The local market town of Mold is 3 miles and the old walled city of Chester is 14 miles.