From Abingdon you can follow the National Cycle Network south towards Sutton Courtenay. This is signposted, but work is still in progress. Look out for signs with a bicycle symbol and a red "5" (Route 5 of the NCN). 

Starting from outside the Guildhall, the route is East St Helen St, St Helen's Wharf , LEFT onto Wilsham Rd (following the river), West Quay and past the sports ground. A tarmac track starts by the sewage works (494951) leading to the Peep-o-Day lane bridleway (starts 493947) to Drayton Road. The NCN turns left here, to Sutton Courtenay and Didcot. For Harwell, turn right towards Drayton and then left to Milton Village.

There are two choices from Milton village.

If you wish to avoid the Milton Interchange roundabout there is a bridleway (starts 487925) that takes you past Milton Manor and under the A34 to Steventon. From here you are stuck with the climb out of Steventon and the traffic lights at the A4139 junction. The bridleway is a pleasant route though- being an ancient cobbled road and is great for journeys involving the Fox.

The most direct route requires that you cross Milton Interchange. This is not pleasant, you may prefer to get off and go around like a pedestrian. However, it is not very nice for pedestrians either. (Milton Park are planning some safer crossing facilities here.) However, it is worth spending a few minutes crossing here to benefit from the directness and quietness of the road from Milton Heights to Milton Hill which is quieter than the A4130 and avoids the traffic lights. If you have crossed the arms of the roundabout on foot, it is easier to use the zig-zag path that goes from the northbound A34 slip road into Milton Heights (~483913). From Milton Hill, by the Packhorse, it is the A4130 to Rowstock then A4185 up the hill to the Harwell Campus.