I spent two nights in Cuenca, about 1-1/2 days. I am a slow traveler but walk fast, if that makes sense. I tend not to get started early in the morning, so someone else could probably cover what I did in one full day.
I did Cuenca entirely on foot, and I walked every street in the medium-sized historic district. The best view of the hanging houses is from outside the historic district, on the other side of the river or from the footbridge.
I also visited the cathedral, which was very chilly even though the weather outside was quite hot that day. The cathedral has an English-language audio guide (pretty common in Spain), and from my experience you spend more time in churches when you're using one of those devices.
There are three modern-art museums/galleries in Cuenca, and I visited them all. The Spanish Museum of Abstract Art and the Fundacion Antonio Perez are somewhat larger than you would expect, given Cuenca's size. Both of those are in the historic district; I liked them both a lot. There is a third display space, I think in the same building as the parador on the other side of the river. I thought that one (with far less on display) was imminently skippable.
The slow trains arrive close enough to the historic quarter to make walking viable as long as you're a good walker and don't mind that the last part of the walk is distinctly uphill (hill town; of course it is). There is a bus that goes up there, but I think it is more frequent on weekdays. The AVEs use a different station farther from town, and from there you'd need to take a bus or a taxi.