As a recent job hunter, I am interested in construction employers within a specific region. How can I find these construction employers without wading through the countless positions with the big job boards who do not provide region specific data?

You can find the construction employers you're looking for at the library. Ask the reference librarian to help you track down information about local construction employers. That's what reference librarians do: help you find what you're looking for.
Once you identify the construction employers, start searching the major business publications to learn more about them and the industries they're in. This is where you'll start identifying opportunities (and names of key managers).
The Motley Fool is a great place to dig up useful info on lots of construction employers. Check the Fool's Investment Ideas feature to research industries and look up the 10K reports of the construction employers you're most interested in -- use the SEC's EDGAR data base. Learn to use the library effectively. You'll find stuff (and expert help) there that you can't access on the Web.