I know around the mid 1800s that a bunch of Chinese headed west to California, but as my knowledge goes, it was almost entirely economic reasons happening within China and the gold rush. And being very poor at geography I can only guess that the far east of Russia was just 'too cold' to permit larger travel (Vladivostok's port was only active during summer and built only after the gold rush had already ended). Plus it likely wasn't economically suffering as much as China.
But are the reasons as simple as that? Surely some Russians had emigrate in decent amounts. This is a question that's been bothering me since highschool but have found extremely little on
Migration from the Russian Empire to the United States was mostly during the "Ellis Island" period of immigration (1880-1920). It should also be noted that many of the immigrants coming from Russia are not necessarily remembered today for their national origin, since they were often either Jewish or German speaking - and they were not necessarily recorded in immigration documents as Russian, and might not have identified that way. However, as country of origin, there were indeed a very large number of immigrants from Russia and they were the third largest group by country of origin in the 1920 census at 1.4 million.
Immigrants from Russia tended to follow the immigrant channels from Europe across the Atlantic to the Eastern ports, rather than to the West. If you look at even the modern population distribution in Russia you will see that the population is heavily concentrated in the East. There simply was not much population in the West and no established immigrant route from any Western Russian port to the American West Coast. In comparison the Chinese population was huge and there were existing operations to recruit and transport Chinese labor - for example to Caribbean islands as a substitute for slave labor after it was abolished by the British. This link gives a very brief introduction to the background Chinese labor migration along with sources for further reading: https://cla.umn.edu/ihrc/news-events/other/coolie-trade-19th-century
Not all of the immigrants settled along coastal cities. If we take the "Mountain" and "Pacific" regions to be the "West" then there were about 70,000 immigrants from Russia in the West in 1920. That includes everything West of Colorado - the main destinations were Colorado and California. However, if you expand your definition of the West there were also quite significant numbers of immigrants from Russia in the Dakotas, Minnesota, Nebraska, and Kansas (about 80,000-90,000).
These are small numbers in comparison to the size of the immigrant population in New York (530,000), but as a proportion of Western immigrants they were quite substantial. In Colorado they were one of the the largest immigrant groups. Depending on your definition of the West we might say around 5-6% of immigrants in that region were of Russian origin in 1920 (a little less than their 10% share of the immigrant population in the whole US).
For more data check out the 1920 census figures on foreign born population by country of origin: https://www2.census.gov/library/publications/decennial/1920/volume-2/41084484v2ch08.pdf
