Veterans Residential Care Choice Act This bill authorizes the Department of Veterans Affairs (VA), at the request of an eligible veteran for whom the VA is required to provide domiciliary, nursing home, adult day health, or hospital care, or who is determined to be in need of such care, to place the veteran (at the expense of the United States) in a state licensed or certified residential care facility that meets VA standards if the cost of providing such care through the facility is less than the cost of providing the care through any other available option. An eligible veteran is a veteran who is eligible for hospital care or medical services based on: (1) specified service-related disabilities, (2) who is a former prisoner of war, who was awarded the medal of honor or who was awarded the Purple Heart; (3) who is a veteran of the Mexican border period or of World War I; (4) who was exposed to a toxic substance, radiation, or other conditions; or (5) who is unable to defray the expenses of necessary care.