I only had a day to spend in Charlotte, and I thought this museum gave me a great sense of the city's history. The museum focuses on different transformations that the city has gone through to reinvent itself (from slavery-based cotton plantations to textiles, and from textiles to finance).
The museum is very well put together, and the initial video introduction does a great job of establishing context for the rest of their exhibits. There was also a temporary exhibit about the desegregation of schools, but I didn't have the chance to check it out.
Charlotte has quite a few other museums in the downtown area (a couple art museums and Nascar HOF), but if you're goal is to understand the very city and state that you're visiting, then I highly recommend the Levine Museum of the New South.
Side-note: It's nice to find a Jewish-named museum that's not necessarily Jewish-themed.