Great city!! You'll find not only historical sites, and squares, gardens.. but also great malls and amazing restaurants. If you like sea food, you must go to the central market - like an open fair, but in a historical bulding. near down town. I had King Crab - Centoia - in the El galeon restaurant.
We stayed in the Hotel Galerias (http://www.hotelgalerias.cl/) - near downtown. Is good for visiting the historical sites during the day. But to go to a good place to have dinner, you should get a taxi. the malls are quite far... like 20-30 min. but it will cost 16 usd - more or less.
The hotel had a great price and really good service. the breakfast also was great!! I really recomend. The only bad part is the location for the night.. but the other good neighborhood to stay is Los Condes or Previdencia. and there, during the day you should get a taxi to visit the historical sites downtown. so... you choose!
There are many parks in the city, worthy the visit - Cerro Santa Lucia, Cerro San Cristóbal, and many squares.
Cerro San Cristóbal
We also visited Valparaíso and Viña del Mar. Like an hour drive from Santiago to the coast. We got a tour from viator web site http://www.viator.com/. They pick you up at the hotel and give you a great tour!! the chilean company they use is called Turavion - http://www.turavion.cl/.
Valparaíso Harbor - second largest of Chile
Valparaíso - Muai ( from easter Island)