Try updating your hosts file (for windows users @ c:\windows\System32\Drivers\etc\hosts) with an entry that will route all requests from your live domain back to your machine.
So 127.0.0.1 mywebappthatusesfacebook.com.
Then make sure that your app is running at the root of your webserver. @ http://localhost/ Then goto mywebappthatusesfacebook.com in your browser and it should redirect right back to your local machine. Facebook won’t know the difference. Hope this helps