If you're looking for good public transportation, you're not going to find it anywhere in the Southeast, especially in North Carolina.
Maybe look further north to the DC/NoVa area if you absolutely need public transit and would like to stay in the general area. Otherwise you will need a car no matter what southern city you're in. Charlotte has a light rail, but it is limited to the downtown proper, or what they call 'Uptown.' You're also going to notice the total lack of sidewalks and bike lanes on many major roads. This is something that is exclusive to the South. Here, we don't like investing in infrastructure, so the most you're going to find would be Greenway systems in more liberal areas, which are also limited to the Charlotte area (Primarily Mecklenburg County) and one other area of our state, The Triangle.
The best area in the state for walkability and cyclists would be the Raleigh, Durham, Chapel Hill area because there are hundreds of miles of Greenway and more 'bicycle friendly' communities, however, public transit is worse there than what is provided in downtown Charlotte.
Overall, my advice to someone else who loves public transit and walkability would be to consider some other cities outside of the Southeast. There are cities in the Northwest with a little bit of a higher cost of living, but with extensive public infrastructure, public transportation, and less traffic due to their public transit. To many people in the south public transit is seen as poverty buggies so they don't really invest in it and treat them like they actually are poverty buggies.
I love the area that I'm in and I don't really mind the lifestyle I live. But, before you move you must come to terms with the fact that things are the way they are in the south and there is little you can do to change that. I would know, I've lived in NC my whole life (Charlotte and now Raleigh) and I have traveled extensively to other cities throughout the United States. Trust me when I say that if this is important to you, don't bother moving here.
Incoming down votes from people pretending public transit is a viable option in the south.