I live in Charlotte, not sure what to tell you to do on a Tuesday. There's the man made whitewater center if you're into rafting, or Lake Norman is a good place to go on a nice day (but it helps to have a boat). If you want a shitty amusement park you can go to Carowinds a little south of town. The NASCAR hall of fame isn't open yet so I guess you'll miss out on that. Downtown (or Uptown as they call it here) is ok to see, there's lots of restaurants and it's got a decent skyline. Not really sure what you're into or how long you'll be around but feel free to PM or ask any questions.