GIT and Development URL’s point to production

I am experimenting with GIT for version control. I have a production environment that I created a repo for HERE, then did a git clone locally. I created/modified the wp-config to work with my local DB. The index page loads, but all of the links for any pages or post point to the production URLs.

How can I make this so running the local instance allows me to browse to all the local pages/posts?

I would use WP DB Migrate to export the DB in the production environment. It allows you to rewrite URLs. Then you import that in your local DB.