You HAVE TO go to the salt flats in Uyuni, Bolivia. This is a must see. I have traveled a solid amount in my day: 30 countries spread over 5 continents. THIS trip has got to be the most memorable of all. I'll leave out the detailed explanation of my experience – Go see for yourself. I will, however, tell you how to get there and back safely, and most importantly, what not-to-do.
I live in Buenos Aires, so I am going to tell you how to get to Uyuni from here. Other pre-destinations typically include San Pedro de Atacama (Chile) or La Paz (Bolivia). From BsAs, the best way to start your trip is to buy an overnight, one-way bus (micro) ticket from Retiro station to either Salta or Jujuy. This trip takes anywhere from 17-21 hours. Most of these buses leave Retiro in the evening, and arrive about the same time or a little earlier the next day. I recommend coche/cama (which basically means very comfy seats that fully recline). Argentina is known for having some of the best buses in the world, so spend the extra 40 pesos and go for it. However, if 40 pesos is not something that is worth spending on a better bus meal and more comfortable travel, the semi-reclining buses are very nice as well.
When you get to Salta or Jujuy, the best thing to do is cab to a hostel for the night. Some people spend time in these two places and then make their way to Bolivia, but if you're heading straight for the salt flats in Uyuni, don't worry about it. Just make sure to write down the name AND address of a couple solid hostels. Cab drivers in Salta and Jujuy tend to not know exactly where these places are. Both places are fairly big too, and only a few hostels are within walking distance from the bus terminals.
Salta: If you're just staying the night, a very nice a comfortable hostel that is located very close to the terminal is La Salamanca Hostel. Ignacio and Pablo will make you feel right at home, and there are great computers with high-speed Internet.
La Salamanca hostel - Right in the heart of Salta, we offer all our guests comfortable accommodations and warm, friendly service.
If you are staying in Salta for a while, try to get there for the weekend. Usually Friday and Saturday are packed with people, and a couple streets are shut down for people to safely walk from bar to bar. The Salteños are nice and friendly people. 2 great hostel options for an extended period of time are CorreCaminos Hostel and Prisamata. Literally Corre Caminos is your fast-paced party hostel with a big pool, and Prisamata (Hurry Kills) is laid back with about 6 hammocks to share. Ramiro at CorreCaminos is the man, and the Prisamata entourage will keep you in Salta way longer than you planned.