Toledo and Segovia are the most popular day trips from Madrid and easily reachable by train. Ávila only takes a couple hours to see so it would be possible to visit both it and Salamanca on the same day since they are along the same train line.
A place closer to Madrid that not many visit is Alcalá de Henares, the birthplace of Miguel de Cervantes.
If you wanted to rent a car for a day, you could visit any number of the following places, Chinchón, Belmonte castle, Cuenca (hanging houses and gorge), Consuegra (windmills and castle), and Campo de Criptana (windmills that were Cervantes’ inspiration for the giants in Don Quixote). They are all within 1.5 hours of the airport and it would be fairly easy to see any two or three on a long day.
For a nature site, north of Cuenca is La Ciudad Encantada with unique rock formations.
If you really enjoy castles there are nice ones in Medina de Campo, Coca, Portillo, Cuellar, and Peñafiel if you want to go castle hopping.