Las Grutas and Taxco are both easy day trips from Cuernavaca even though they are in the state of Guerrero. You could do them both with a car or a tour if you start early. I would not try Las Grutas via bus. Hard to tell what you'll find in Taxco and you might easily spend a day there.
The Grutas de Cacahuamilpa National Park in Guerrero, Mexico, is best known for the Grutas de Cacahuamilpa Caverns, which are one of the largest cave systems in the world. It is also home to the Grutas of Carlos Pacheco, a smaller system, as well as two subterranean rivers which have carved out tunnels in the rock. The park has extreme sports attractions such as rappelling, and rock climbing in Limontitla Canyon. as well as the two underground rivers to explore. It also has a small botanical garden, a pool and places to camp.