For a work project I’ll likely be spending a couple of evenings in Kent regularly over the next few months, so would like line up some riding if I can. We’re talking evening rides after work BTW – a short drive to ride would be manageable during the light summer evenings I think but riding straight from work / hotel (Manston) would be ideal.

Is this purely road bike territory or is it worth taking a CX / mountain bike?

Any recommendations on where to go / what to do ?

The Viking Trail

This is a pretty decent route and would be perfect for a CX bike.
I rode it a couple of years back on my Giant road bike and that was OK.
You don’t have to do all of it, as you can jump on/off at many different points.