I would start one real public hospital to show how it's done or would look. I would demonstrate a single-payer system with one hospital first and make the books public. The state would buy the equipment and pay the employees and see patients first come, first serve. It wouldn't be income restricted or charge anything, it's an experiment and a public service.

Figuring out where to put it would depend on a few things, and it might be easier to buy or work with an existing hospital, but I'd seek to have that set up in the first year so it runs for at least three years.