Look into joining NC PDRA.
Piedmont Diving and Rescue Association It owns 3 quarries in the Piedmont area and since you're in Greensboro, one of them is just outside of Yanceyville (JMR quarry) and would be reasonably convenient to you. It is small as far as surface area goes but is around 90+ feet deep. Last time I was there last year I was pushing going into deco. I'm not a tec dier so avoid deco.
Another quarry PDRA owns is at Lake Norman just outside of Mooresville. It's a bit larger than JMR bu is maybe a little deeper. Unfortunately, it has been closed for a couple of years as they are trying to eradicate a zebra mussel infestation. Currently, there is no planned reopening date.
The third one is American Quarry just south of Salisbury. It is small and rather shallow at around 45 feet deep overall with the exception of "the Pit" which drops down to 65 feet. Since I live in Thomasville, this is the closest to me and is thone I go to the most.
You can join by going on-line and filling out an application form and paying a membership fee. There is a small application fee to pay but you only pay that once just as long as you don't let your membership lapse. You'll then receive your membership card(s) and gate key(s) which gives you 24/7/365 access to all 3 quarries ( except, of course, the Lake Norman quarry at this time.
Another local quarry is Blue Stone Dive Resort just outside of Thomasville. It has a rather large surface area with a depth of around 50 feet but does drop down to around 90 feet in one area. Blue Stone is a privately owned quarry and does required an entrance fee each time you go. It is, however, a full service facility with air and nitrox fills, gear rentals, gear service, etc.
Other than Mystery Lake
@Bjparris1990 mentioned, these are pretty much going to be your only options short of going to the coast to do some wreck dives, of which NC has an abundance. But that can get rather spendy, especially to get to the deeper wrecks. But there are some great wrecks to dive off the NC coast.