Fort Jackson SC

see http://www.fortjacksonmwr.com/weston/ but your son will have to sponsor you, which could be a trick being he his having all the fun right now. Maybe call the contact in above link and ask how do they handle your type of visitor. Half way down on link page is their travel camp. And getting on base using the "right" gate would also be a question. Just a thought, Your son might not want anything to do with the base and wants out of there?
The last thing I had in mind after graduation was staying on base!
Also see http://www.militarycampgrounds.us/milcamps/50-south-carolina/169-weston-lake-recreation-area-and-rv-park

Hope this helps.