I want to travel from Santiago (Chile) to Lima (Peru). I will not go through Bolivia but I would like to visit the salt flats from the Chilean side. Is this possible? I only want to hop over to the Bolivian salt flats and back. I've heard that the salt flats in Bolivia are really worthwhile so I might want to skip the ones in Chile.
It will depend on how much time you have. Salar de Uyuni is HUGE (10,582 square kilometers), and not only you will need time to get there, but also to see the many different facets of it.
Still, it is possible to visit it from Chile if you have enough time. You can get a train from Avaroa on the Chilean border, but keep in mind the schedule is not exactly trustworthy and times can vary a lot. Also, because you are crossing a border, you will need some extra time for the paperwork.
The best option would be, in my opinion, a tour from for example San Pedro de Atacama. Tours can last up to five days, and they usually include Laguna colorada (a beautiful red lake full of flamingos), the geysers (when I went to had to depart at 5 am to see them, the sunrise is beautiful) and Tupiza (giant columns of clay). They also tend to include delicious meals, (very humble) accomodation and a guide.
I strongly recommend you do it if you have time. It's a unique place, full of unexpected marvels. If you are going to be there overnight, be careful with the temperature changes. At night it can descend drastically (we are talking about -10 or so in the winter), and during the day it's quite hot. Also, don't forget your sunglasses, as the glare can be quite strong.
You can go on a tour from San Pedro de Atacama (in Chile) which takes 3/4 days, visits sites in both Chile and Bolivia and will get you back to San Pedro, for about 200USD.
As an alternative, you can get a bus from Calama to Uyuni, which takes 7-9 hours, depending on border formalities, while the bus only runs by day and only on 4 days a week. The ticket is about 20USD. In Uyuni, you still would have to get a tour operator, but then you would be able to see the important Bolivian sites in one day. This will cost about 20USD. Getting back to Calama would take you another 7-9 hours.
There is currently no operating passenger train between Calama and Uyuni.