They may have good security there, but take heed the suggestions about not going out at night in that area. Apart from Graceland itself, there isn't much else to do or see within the immediate vicinity.
If you don't have to have full hookups, Hernando Point at Lake Arkabutla, about 25 miles south of there near Hernando, MS is a nice QUIET campground. I did my break in trip there and have been a couple of other times just to go fishing or see the lake. If sewer is a requirement, there are two campgrounds in Horn Lake, MS (10-15 minutes south of Graceland) that are clean, have pools, playgrounds,etc., but are just a bit on the high side price wise.