I'll be driving from Madrid airport to Valencia and then from Benidorm to the Madrid Airport. Are there any cute towns that we should stop in for an hour or so each way?
From Madrid to Valencia, you could stop in Alarcón, a cute hilltop village high above a horseshoe river bend, complete with castle (now a Parador) and a church with interesting modern murals. Leave the A3 in Honrubia and drive along the old N3 to Valencia to find it, you drive across a dam (always fun) and then it's a right.
On the way back, to switch things up I suggest you take the AP36 from La Roda to Madrid instead of the A3. Sure there's a toll, but there's NO traffic - it's incredibly deserted. It takes you close to Belmonte castle, which is worth a visit and probably does not take more than 2 hours taking into account the short drive to and from the highway.
On that route, much closer to Madrid, you would pass by Aranjuez where the Palacio Real and gardens are really lovely - but you would need more like 3 hours rather than 1-2.
By the way, why Benidorm? It is a fun place with the right state of mind (think Myrtle Beach, S.C., but even more built-up), and I can't deny that the cluster of beachside skyscrapers is an impressive sight, but it is a very unusual destination for Americans.
Balso’s suggestions are good. If the church in Alarcón isn’t open (check its hours) there little else to see in the town. The castle is nice and a place where many people go for a drink or to eat. It is small. There are few shops or restaurants in the town. The walk around the town affords one a good view of the town and castle.
Belmonte castle is very much worth visiting. Closer in towards Madrid is Chinchón.
Other nice places to consider are Cuenca, Teruel, Medinaceli. and Albarracín. About 30 minutes from the airport is Alcalá de Henares. It’s nice to visit too. Where to stop depends on the route you take.
For idea purposes, photos from our trip to that area are on my website.