Bruce, a suggestion for 1 day.
Hilversum is just 48km (30miles) from Arnhem
Do yourself & your bikes a favour & drive over & check out the fabulous woodland rides around the area, in particular the west side of Arnhem around Oosterbeek. Nothing taxing, just gentle peaceful network of woodland rides & cycle paths, some hard road, some hard dirt (you will need a detailed local map as they are everywhere)
Incorporate it with a day looking into the famous WW2 battle & make it an education & easy ride day - in fact its best way to do a casual airborne visit.
For the casual visitor there is not much to see in Arnhem town apart from the bridge itself (its not the original anyhow). Most all the visitor interest is around Oosterbeek. After a drive around Arnhem town to see the bridge I suggest you park the car for the day at the Hartenstein Airborne Museum (well signposted - west Oosterbeek). The museum & the area around it takes about 1 to 2 hours for a casual visitor.
Then take an 8 mile ride out on the small roads & roadside cycle paths to Ginkel Heath, see the memorial & take a nice lunch at the cafe just opposite. Take the heathland track southeast, or if muddy take the side roads & cycle paths, to Wolfheze, over the railway crossing & sharp left into woods just south of & running parallel to the railway & just wander around (great woodland glades). Meander south through the woods, over the Utrecht road, through more woods down to the river working east along the river bank roads. Then back via cycle paths & road to the car parked at Hartenstein.
Next go to the airborne cemetery - my dad is 30.A.1 - after that leave the area on Dreijenseweg, at junction turn left on Amsterdamseweg (nice evening meal restaurant at that junction) & head home.
Its a nice day out, light riding, added interest & in May the woods are at there best. Camera is mandatory