Generally speaking east Memphis is very safe...or at least it was about 12 years ago when I lived there. Shelby Farms is great for runs. Contact the CBU head coach for tips on the area. They just had their home meet a few weeks ago on the south side of the park.
The Wolf River trails are good. They are not always maintained perfectly, but, tend to be pretty good. There are some pretty good dips and sharp turns. Plus, you may have to fight bikers for the trail since they technically own it.
Lastly, if you want a hilly long run, you can go north to Shelby forest, a state park about 25-30 minutes north of where you'll be. It's right on the Mississippi and you can find all sorts of long runs looping through the area. For a guy like me from track-flat south Louisiana, it was torture.
Additionally, you could run west on Poplar for several miles before you would get into any rough neighborhoods. Once you get past the University of Memphis, it can get rough. So long as you head east to west (or vice versa) on Poplar you should be safe. Don't go north to south.
Contact the Breakaway store in Germantown if you need more info:
http://www.breakawaymemphis.com/Breakaway_Running.html