In my opinion, Nick could be referring to a couple of different ideas.
First, Daisy and Tom are from Chicago, as is Nick. James Gatz is also from that midwest region. The entire storyline revolved around these four characters who were Westerners in that era. They all sought the big city to escape something of the West. For each of them the escape was different. For Tom and Daisy, a extramarital affair of Tom's moved them away from the reputation that he would have had if they stayed put. For Nick, he was restless and sought something more engaging. For Jay Gatsby, he was running toward Daisy, escaping a life without her.
Another idea could be that the West refers to the great ideas that expansion westward was full of material gain. The gold rushes of the 1850s and the rush to the golden rays of California drew attention to the idea that life could be ideal. It could be perfect. All of these people were striving for their perfect in The Great Gatsby but none found fullness in the American Dream because they searched for it without concern for fellow man.