Nuclear Family Priority Act This bill amends the Immigration and Nationality Act to eliminate parents from the definition of "immediate relatives" with respect to those aliens not subject to worldwide immigration levels or numerical limitations. Existing family-sponsored immigrant categories are replaced with a single preference allocation for spouses and children of permanent resident aliens. This bill: (1) reduces the number of, and revises the calculation for, fiscal year family-sponsored immigrant entrants; and (2) establishes a nonimmigrant visa category for an alien who is a parent of a U.S. citizen at least 21 years old.