While having access to a set of wheels, a scooter that we rented for the day, we decided to head inland and visit the Filerimos Monastery. Inland Rhodes is very hilly and still mostly wooded -- you'll need a vehicle to see its highlights and no single site will justify the expense of a taxi or the inconvenience of trying to make due with a sparse bus schedule. Public transportation is readily available along the coast but less so inland.
The monastery is at the top of a windy road and is the same name as the hill upon which it is situated. Filerimos means "lover of solitude" after the 10th-century settlement here by Byzantine hermits. There is not much else to see at this site except for the monastery which was restored by the Italians and British.
If you hunt around, you can come across some ruins of interest is the Doric fountain with a columned facade.
A short walk from the monastery and archeological zone we came across the "Way of the Cross", with 14 stations marked out in copper plaques that lead to an enormous concrete crucifix. If you are not faint of heart, you can climb out onto the cross-arms for a truly amazing view.