What’s your budget like? I lived in Chile for about a year, and there are a lot of great places to visit, and like everywhere, some are more costly than others. The Atacama is really, really cool, especially if you have the opportunity to fly over it. You can see the Nazca lines. But, if you don’t have enough money for a trip like that, or enough time, I’d head south toward Patagonia. One place I really enjoyed was Lago Todos los Santos. It’s been a long while since I was in Chile, but I think it was several hours south of Santiago. It’s this naturally bright blue lake, and when I was there, they offered rafting and “canyoning,” which was really cool. Basically, we got to climb around on waterfalls. Very, very fun. We also managed to climb an active volcano while we were there. I think it was Volcano Villarica, near Pucon. It was really cool - it took us about 4 hours to reach the top, and we got to look into the crater (we didn’t see much - too much sulphur smoke), then on the way down, we just sat on our asses in the snow and slid down - total travel time on our butts: 45 minutes. The trek up wasn’t too bad, but we did have to use snow clamps on our boots and poles, so it may or may not be something you’d like to do.
Also, you might visit the Cordillera - the Andes mountains. There are a lot of fun places to check out up there. There are several lakes up there, and they have boat tours on the lakes.
A fun day trip from Santiago would be to Vina del Mar where Pablo Neruda lived. Vina is about 30 minutes from Santiago, and they have tours of Neruda’s house. It’s also a beach-side resort, so there are plenty of touristy-type things to do, if you’re interested.
When you’re in Santiago, try the humitas and empanadas de pino. Humitas are like corn cakes wrapped in a corn husk - you can put either sugar or salt on them. I prefer sugar, but I’ve got a big, bad sweet tooth. Either way, they taste fabulous. Empanadas de pino are baked and have beef, gravy and olives in them. There are also empanadas fritos, which are deep fried and have ham and cheese inside. Very tasty, too. Whatever you do, have a great time!