Veteran's Choice in Nursing Home Care Act - Allows the Secretary of Veterans Affairs to enter into agreements with non-Department of Veterans Affairs (VA) nursing homes of the veteran's choice to provide nursing home care to veterans eligible for such care through the VA. Requires the: (1) Secretary to pay the non-VA facility for the provision of such care, with payment limits; and (2) veteran who requests such care to assume responsibility for costs that exceeds the VA limits.