If you're looking for someplace with stuff for kids, KOA East would be my suggestion. There are other nicer ones, some closer to Biltmore, but lacking much for kids.
Parking: Just read the lot signage before you leave your vehicle. City surface lots usually have an unmanned kiosk where you pay for the space. Private lots are required to be very visibly signed. Most private lot owners have contracts with towing companies to keep their lots open for their customers, and yes, they will tow. The city doesn't tow except in rare cases of public safety; they just ticket repeatedly.
Jim, "5 out of 4 people have trouble with fractions."