South Texas Veterans Access to Care Act of 2006 - Directs the Secretary of Veterans Affairs to determine, and notify Congress, whether the needs of veterans for acute inpatient hospital care in 24 counties comprising Far South Texas shall be met through: (1) a public-private venture to provide such services and long-term care to veterans in an existing facility in Far South Texas; (2) a project for construction of a new full-service, 50-bed hospital with a 125-bed nursing home in Far South Texas; or (3) a sharing agreement with a military treatment facility in Far South Texas. Requires the Secretary to take appropriate action depending on the option selected.