That was the NC Zoological Park. It is located in Asheboro, about 30 minutes south of Greensboro. Well worth the drive. It is a large park, lots of walking between the exhibits. They do run a tram throughout the park to make it easier. Spring and Fall are my favorite times to go as it can get fairly hot out there in the summer.
I think ticket prices are fairly expensive. We used to have a membership to the zoo, about $60 per year. But my mom gave us a membership to the NC Aquarium which has reciprocal admission with the zoo. For a family our size the membership works out to be about what we would pay for one visit.