Why were Western territories among the first to adopt laws granting political rights to women?
"In 1869, Wyoming became the first territory of the United States to grant general female suffrage, and entered the union in 1890 as the first state where all women had the vote."
Congress required a certain population (500,000?) in a territory before it applied for statehood. Some Western Territories, eager to join the United States, allowed any settler of age to vote to statisfy the numbers requirement. Many Wyoming legislators -- all male -- hoped it would attract more single marriageable women to the region.
After Wyoming, the sequence of suffrage was:
1896 Utah and Idaho
1912 Arizona, Kansas, and Oregon
1913 Alaska Territory, Illinois
1914 Montana and Nevada
1917 New York, Nebraska, North Dakota, Rhode Island
1918 Michigan, Oklahoma, and South Dakota
1919 Indiana, Iowa, Maine, Minnesota, Missouri, Ohio. Tennessee, and Wisconsin
1920 - 19th Amendment
Right before the passage of the 19th Amendment, Woman Suffrage, the rising tide of women voters in the states influenced the passage of the 18th Amendment, National Prohibition.
I think it's also important to note that women were needed for their physical labor and childbearing ability in areas where farms and society were being started. Starting a successful farm or ranch is a very physically intensive enterprise. It requires the work of both men and women. Plus, in an agricultural society, the more children one had, the more people there were to work the land. Thus women became important economically. With that importance, it was easier for them to demand more equal treatment, including the vote, than in some areas where parents still paid a dowry to a man just to marry a woman. When one is important to the economic well-being of a society, people tend to give her more respect.