Cantavieja is a small village and its specific sights can be quickly seen. However it’s a vital link in the circuit Valencia – Teruel – Maestrazgo – Castellon – Valencia, better described under Teruel. At least done in this direction, the circuit entails a night spent in Cantavieja and that’s no hardship. The narrow streets of the old town grow on you rapidly and it’s good to just stroll around, even though the hilltop location induces mighty winds.
Some of the houses are built immediately over a sheer rocky precipice but you will need to take quite a walk to see this from below. If staying longer, you would doubtless find many good routes into the Maestrazgo mountains.