There’s a nice 15-20 mile loop that starts from Wye and runs through the edge of King’s Wood, Chilham and Crundale that’s well worth a visit in the Spring/Summer.
The local trails are on chalky soil, which is pretty offensive in the Winter months, but once it dries out it’s quite agreeable to ride on. It’s flinty too, so make sure that you’re running durable tyres.
There’s some nice jumpy stuff around Perry Wood, but the local ramblers really don’t like you going off-piste and can be objectionable even if you stick to bridleways. Otherwise, there’s Blean Woods just outside Canterbury, which isn’t too shabby.
The local area is crying out for a dedicated bike park – King’s Wood would be ideal as it drains reasonably well and has a network of fire roads.