Since you'll be downtown, my pick for nearby authentic Texas cooking would be the Dixie House in Lakewood. Get the chicken fried steak.
And yes, there is a Southfork. At one time, it was right up there with the Alamo as the most popular tourist attraction in Texas. Nowadays, it mostly hosts corporate events. It's in Parker, east of Plano. Figure an hour drive from downtown Dallas, or 90 minutes from DFW (non-rush-hour).
www.southforkranch.com