Hello there! :)
I have a few suggestions for ya’!
Hagan Stone Park (near Pleasant Garden) – My family actually stayed here for quite a few weeks while in search of a house. We loved it! It was clean, affordable, and there are playgrounds and such of you have kids! Go here for more info – http://www.greensboro-nc.gov/Departments/Parks/facilities/reservations/hagan.htm

Greensboro Campground – Had several friends who stayed here – they loved that it had wireless internet!
http://www.greensborocampground.com/

Hope this helps!!