During the mexican-american war, the united states and mexico fought over land in the northwest. land in the southwest. independence for mexico. payment for california.

Correct  Land in the Southwest

Context/detail:

The Mexican Cession was territory ceded (meaning given up) to the United States in 1848 after the Mexican-American War.  The territory included lands that represent the full states of California, Nevada, and Utah, as well as large portions of  Arizona and New Mexico, and about a quarter of what would become the state of Colorado.  There was also a small section of Wyoming involved.  So that represents the bulk of territory that is in Southwest of the present United States.