Fred, welcome to Charlotte and the Arboretum area. You'll find a number of options for shooting in the area.
You will find USPSA matches in Statesville, Salisbury (Rowan County), * Lake Lure (Asheville area) NC and Columbia, Spartanburg, & Greenville SC. Farther east you have Creedmore (north of Raleigh) and Ft Bragg (Fayetteville).
Besides the two 3 gun matches mentioned, there are a number of unaffiliated 3 gun matches in the area.
There are at least 3 clubs in the area that you might consider for training but don't host USPSA matches. As well as a number of indoor ranges with very restrictive shooting rules.
Hope that helps.