Taff Trail
The Taff Trail is a multi-purpose route between the Market Town of Brecon in the North and the Cardiff waterfront at Cardiff Bay in the South. 55 miles (88km) in length, it passes close to Pontypridd and Merthyr Tydfil and through a wide variety of urban and suburban landscapes of those towns and the open moorland of the Brecon Beacons. There are also many “green fingers” where the Taff Trail itself appears to bring the countryside into the town. The area is also rich in industrial archaeology.
From Morganstown you can join the Taff Trail via the access at Gelynis Farm. In Radyr a trip under the railway line beside the station and then over the river bridge will get you onto the traffic free trail all the way into the centre of Cardiff.
Website: http://www.tafftrail.org.uk/
Information from Sustrans: https://www.sustrans.org.uk/find-a-route-on-the-national-cycle-network/cardiff-to-castell-coch/