Visit Las Termas de Cauquenes and enjoy a nice thermal bath from naturally hot springwaters. Located 31 km east of Rancagua, the surrounding area also offers pretty trails for easy hiking (http://www.gochile.cl/spa...).
Reserva Nacional RÃo Los Cipreses is a national park east of the city, towards the Andes. Great for overnight camping. Be sure to arrive early however, as you won't be able to get in after the 6pm closing time.
Take a tour of the now defunct mining town of Sewell now a UNESCO World Heritage Site, situated right on top of El Teniente, the largest underground copper mine in the world. Private tour agencies can take you to the town, the mine, and back (http://www.sewell.cl/engl...). If going there by car, keep in mind they only let vehicles manufactured after 2001 through.
Go to a division 1 football match as the O'Higgins football club calls Rancagua it's home.