I also use rvparkreviews.com to lookup campgrounds
For your Greensboro stop, I can suggest Oak Hallow campground in High Point. Its not Greensboro, but just a hop/skip away. From I40 east of Winston Salem, you can take US 311/Future I74 down to High Point and exit on Johnson St to get to Oak Hallow. When you leave, take 311 to I85 or Business I85 North back on your route. The cg is owned/operated by the city and the rate is $35 per night. They do not take reservations.
http://www.highpointnc.gov/pr/oak_hollow_campground.cfm