The Grutas de Cacahuamilpa lie about 30 kilometers north of Taxco, and they are among the largest cave systems in North America. The accessible galleries run for two kilometers through chambers up to 90 meters high, lit and walkable on guided tours that leave regularly throughout the day. The scale is genuinely disorienting — the largest chambers are the size of cathedrals, and the formations have been accumulating for millions of years. Guided tours only; independent entry is not permitted. Tours take about two hours and cover the main galleries. A taxi from Taxco takes about 40 minutes.
Xochicalco is a pre-Aztec archaeological site about 45 kilometers north of Taxco, roughly an hour by car or bus via Cuernavaca. It was a major political and religious center between roughly 650 and 900 CE, built on a hilltop with a clear defensive purpose. The Temple of the Feathered Serpent, carved with elaborate astronomical symbols, is the centerpiece, but the whole hilltop is covered with plazas, ball courts, and residences — you need two or three hours to do it properly. The site has a good small museum at the entrance. Combine it with Cuernavaca if you want a full day out.