The Sustrans national cycles routes will bring you to into the centre of Abingdon; your journey will take you through peaceful and rolling countryside. There is some road cycling and the route through Radley and also towards Milton Park is less suitable for children now with volume and speed of traffic.
The local cycle route the Hanson Way runs from Oxford to Didcot via Abingdon. Until April 2020 note there is a diversion in the village of Sutton Courtenay which adds an extra 2 km and involves some road cycling. Hanson Way is part of Sustrans national route 5. This links with the Oxford cycle ways and the tow path on Oxford Canal to Banbury and Stratford-upon-Avon.
Footpaths including the Thames Path at Abingdon are not for cyclists. Cycle route 5 and walkers’ national trail are separately marked from the wooden bridge near Abingdon Weir. You can get advice from the National Trails office but in general cyclists can use the footpath on stretches that are tarmac or asphalt providing they give way to pedestrians. Where the path is earth or grass this is for walking only.
Cycle route and footpath maps are on each County Council’s information. The diversion during Spring 2020 can be viewed.
Abibike have very kindly put together a map of the bike racks that are avaiable to use in Abingdon:https://umap.openstreetmap.fr/en/map/abingdon-centre-bicycle-parking_451450#17/51.67178/-1.28210
(Accurate as of Autumn 2020)