The first things that comes to mind are Pablo Neruda's three homes. One is in Santiago, one is in Isla Negra and one is Valparaiso. Pablo Neruda was a famous poet and politician in Chile.
Also there are two "cerros" in Santiago that are very famous. One is Cerro San Cristobal and the other is Cerro Santa Lucia. They're both really touristy locations. The "Cerros" are giant hills with various things on them. Cerro San Cristobal has a giant statue of Saint Christopher, some shops and a little thing that's kind of like a ski lift that takes you over part of the cerro. I also think you take a special ride/elevator thing to get up to the top of the cerro. Cerro Santa Lucia has this beautiful building on it, and is right across the street from one of the cities big "ferias," or street fairs. At the street fairs you can buy all kinds of little trinkets, clothing, earrings, jewelry, etc.
The deserts of the north are also very beautiful. San Pedro is a major tourist destination city in the north.
In the south, there are a number of beautiful cities, as well. Right now a lot of these cities were hurt badly by the earthquake. If you want to go pretty far south, Chiloe is an island off the coast of Chile that you have to take a ferry to get to. It's just touristic and pretty far south, and beautiful. Pucon is a city that's kind of rich and fancy in the summertime, also south of Santiago. It has a huge, beautiful lake, a cute downtown area, and one huge hotel that has a casino.
In general, the north of Chile is full of deserts and the south is full of water: lakes, rivers, the ocean, etc.
It's a beautiful country!