Cerro Santa Lucia (Santa Lucia Hill) - In 1541, Santiago was founded on this hill (cerro) and today it is a large park. Start at the water fountain along the Alameda, then climb up the curving stairways to the top of the hill, which is the Plaza Caupolican. If the kids don't feel like walking up, take the glass elevator. From the top, there are great views of the city and of the mountains on a clear day. In summer, there are concerts in the amphitheater.
Artisanas (handicrafts) markets - Handicrafts markets are always entertaining and fun to explore. Try the Centro Artesanal de Santa Lucia (south side of the Alameda), Pio Non (jewelry and children's toys) or Los Dominicos in front of the Igelsia San Vincente Ferrer de Los Dominicos).
Museo de Santiago - The Santiago Museum is housed in an 18th century colonial home, the Casa Colorada. The museum presents a history of the city with absolutely wonderful dioramas. The diminutive dioramas have hundreds of beautifully carved and painted wooden figurines by Rodolfo Gutierrez. Don't miss the model of the Casa Colorada, furnished as it was in the 18th century.
Museo Chileno de Arte Precolombino - The Pre-Columbian Art museum has a large collection of artifacts from all over Latin America, including Maya, Olmec and well as Andean and Chilean indigenous peoples. Look for the blow guns and darts.
Correo Central (Central Post Office) - The Correo Central at the Plaza de Armas has a Postal Museum on the second floor. You'll find a good collection of stamps from all over the world and postal paraphernalia.
Mercado Central - The Mercado Central, an elegant wrought iron metal building, was once the wholesale food market, but is now a fish market with seafood restaurants and fruit stalls. After you've visited the Mercado, take a stroll in the Parque Forestal, a long narrow park along the Rio Mapocho with nice fountains along the way.