I have changed the topic of your question from "Literature" to "Into the Wild" (where I believe it more specifically belongs), and I have added the title to your question so other students can have an easier time figuring out the work to which it belongs. I think, perhaps, the reason why your question hasn't been answered yet.
Your question begins with the character of "Alex" and it's important to realize that Alex is actually an alias for Chris McCandless. Those unfamiliar with "Into the Wild" may not be familiar with this. Now that we have clarified that "Alex" is really "Chris," we can get to the meat of what you are asking.
In regards to your question, "Where did Alex stay outside of Salton city?" the answer is simply "a campground." The explanation of how we know this is quite intricate, however. You see, Alex/Chris was actually staying in a homeless camp for a while outside of Salton City, but I don't think that is what your question is referring to. At this point in the story, Alex/Chris leaves the camp to go back into the city to pick up his final fast-food paycheck.
While his friend and father-figure Franz originally scoffs at Alex's/Chris' advice to experience nature to its fullest.
Mr. Franz, I think careers are a 20th century invention and I don't want one.
Despite Franz's original feelings, after considering the original quote above, and after Alex/Chris goes "into the wild," Franz decides to take Alex's/Chris' advice, buys a camper, and takes the exact spot that Alex/Chris used to occupy outside of Salton City. And, in fact, Franz stays there waiting for Alex/Chris to return until Franz hears of the death in the wild. At this point, Franz loses all hope in life and even in religion.
Two years he walks the earth. No phone, no pool, no pets, no cigarettes. Ultimate freedom. An extremist. An aesthetic voyager whose home is the road. Escaped from Atlanta. Thou shalt not return, 'cause "the West is the best." And now after two rambling years comes the final and greatest adventure. The climactic battle to kill the false being within and victoriously conclude the spiritual pilgrimage. Ten days and nights of freight trains and hitchhiking bring him to the Great White North. No longer to be poisoned by civilization he flees, and walks alone upon the land to become lost in the wild.
In conclusion, more than the "where" did Alex/Chris stay, is the "why" he stayed there. Alex/Chris never felt comfortable in the confines of human society, which, in my opinion is why he goes "into the wild." We can see some of that "why" hidden in the quotation above. Note the words "poisoned by civilization." No doubt he felt that way in every town, even Salton City. As for the Wild. That is the place Alex/Chris felt comfortable, the place he lived, and the place where he died.