What was the first state to let women vote in national elections?

Technically it was New Jersey, but that right was taken away from New Jersey women in 1807. Wyoming became the first place to let women vote where that right was never taken away. The story is complicated ,so see the details below.

New Jersey granted women the vote under the state constitution of 1776, New Jersey women lost the vote in 1807

The territory of Wyoming passed their suffrage law on December 10, 1869,. This became the first time the right to vote for women was protected by law and was never taken away. Wyoming became a state in 1890, and the suffrage law just carried over into its state constitution. Although suffrage was granted to the women of Wyoming first, Utah was the first place where women were allowed to vote under the law .

The territorial legislature of the Utah Territory gave women the right to vote on February 12, 1870 . The first woman voted on February 14, 1870, after both Wyoming and Utah had granted suffrage to women, but before Wyoming had held a election. Thus Utah was the first place where a women voted, and her right to vote was protected and allowed by law. However the United States Congress disenfranchised Utah women, and took away their voting rights, with the Edmunds-Tucker Act of 1887. It was not until Utah was granted statehood in 1896 that women were again allowed to vote.

In 1893 the state of Colorado adopted an amendment granting women the right to vote.