As Scotroutes says there’s the Deeside way if you want to go along between Aboyne and Ballater. If you want to go out the other side of Ballater there’s a route called 7 bridges that is cycle-able as far as I recall.
If you want to have a fun hour on trails have a look at Tarland Trails – there’s 3 runs graded Blue, Red and Orange and a fun pump track suitable for all ages/abilities. There’s also a mini bike park in Aboyne that might be with exploring.
You can also cycle out from Dinnet round Lock Kinord and back – some sections of that are quite rock strewn though depending on which of the routes you take so you might want to walk it first just to see what it is like.