An old hospital near the Presidio in San Francisco will be used as an AIDS hospital under the defense appropriations bill approved by the Senate and the House last week. The measure now goes to the White House, where it is expected to be signed into law. It requires that the old Public Health Service Hospital, owned by the Army, be leased to the city of San Francisco for 10 years, beginning in January, 1989. The city will pay part of the cost of running the facility, but will have virtually no other costs, officials said. The hospital is one of several projects in the $296 billion bill, which includes $91.8 million for various Bay Area programs.