The North Carolina Zoo in Asheboro, NC ( http://www.nczoo.org/) opened in 1974. It is well-run and a pleasure to visit, although on nice days it can be very crowded.
Most people just get a day pass and blast through as fast as they can. That's an exhausting undertaking (even using the trams), since the zoo is about a mile and a half end-to-end. We have a membership and visit several times a year, picking a couple of exhibits to watch over a period of time.