What is the real cost for a public company to issue stock? For
example, what is the real cost to a publicly held company to issue
shares of stock with a market value of $500?

This question is not answerable.

You must clarify.  
Do you mean a company that is already public and they want to issue more stock?

When you say for a share price of $500, that is not really relevant,
you should be providing the entire amount that is intended to be
raised.

The two major costs are legal/regulatory costs and underwriter costs. 
underwriter costs are the big one.  These costs vary depending on the
type of offering they do.