If it's difficult to fit them in your packing, don't worry about it. If you can at least get the kids' bikes in, better safe than sorry.
Our first trip was Jan. '06 and all my boys wanted to do was hit the parks. If you can go all day (and we surely did), when you do get back to the camper, they'll be too pooped to go riding. But if you head back early enough to do some grilling or something similar, it's a pretty safe area to let the kids go riding instead of standing beside you saying, "When's dinner gonna' be ready?"
Where you guys from in NC anyway?