Chile is a land of volcanoes, lakes and hot springs. The earth image you've included are part of the massive volcanic group that form the Andes.
Cajon del Maipo is the closest to Santiago, less than an hour away, and a very popular area with the locals. Within the canyon valley are the Volcán Marmolejo, Volcán San José, and Volcán Maipo.
Lonely Planet offers excellent guidance, and has great options for your adventures with youngsters (and middlesters and oldsters).
Rich greenery lines the steep, rocky walls of this stunning gorge of the Río Maipo. Starting only 25km southeast of Santiago, it's popular on weekends with Santiaguinos, who come here to camp, hike, climb, cycle, raft and ski.
You can get there by bus from Santiago, according to the seasons: as far as San Gabriel in the winter, by late spring and through the summer months, they reach Los Valdes. They depart every 30 minutes from Estacion La Florida.
In Santiago, Tourist Information offices are in Casa Colorada at Merced 860 and at Cerro Santa Lucia in Terraza Neptuno.
The official web site of the Chilean Tourism Promotion Corporation has a wealth of information to help you plan.