We are interested in a day or overnight trip from Valencia (home base) to Cuenca by car. Any guidance on the route, interesting stops along the way, etc ?
ViaMichelin (said to be optimistic) estimates the one-way driving time at 2 hr. 55 min. by the fastest route, so you wouldn't have much time for other stops unless you spent the night somewhere. If you zoom way in on the VM map I've linked to, especially scenic roads will be marked in green. I will again recommend Teruel and Albarracin. You can see an obvious loop on the map. I haven't checked the driving time, and I wouldn't be surprised if the roads are slow-going. But there is a lot of green there.
I think decent visits to Cuenca, Teruel and Albarracin would require at least two nights on the road.
I’ll second acraven’s Teruel and Albarracin suggestion. Teruel is 71 miles from Valencia and it’s all interstate driving on the A-23, speed limit 120kph (72mph). Albarracin is 18 miles from Teruel and Cuenca is 58 miles from Teruel. The road to Cuenca from Teruel (N-420) is a good road, but only 2-lanes with a shoulder, so you may get stuck behind trucks, tractors, or slow cars. The speed limit on it is 100kph (60mph). I drove part of the route in the link acraven sent, back in 2014, from Requena to Cuenca, and there’s nothing along that route worth stopping for. The road to Albarracin from Teruel is also 2-lanes with no shoulder, speed limit 90kph (54mph). In you decide to spend a night in Cuenca, I recommend the Parador. It has some free parking, and a pay garage. It is located just across the gorge and pedestrian bridge from the hanging houses and about a 5 minutes walk to the main historic center. It is in the former convent of San Pablo. There are speed cameras, so stay at or below the posted speed.