since you're not worried about good schools check out this link, you can just click on rentals and your price limit.....after you see what's there you can see if the neighborhood is a safe one.....PM me if you can't find out on your own, I'll do what I can to see where it is, my husband knows the area really well and should be able to give an idea.
http://www.4fayettevillehomes.com/MLS.html
Even though you don't need to worry about schools, you may want to just search in High schools (hold ctrl to pick more than one) Jack Britt Terry Sanford and Southview. In general that should get you in a "safe" neighborhood (Terry Sanford would probably get you closest to work)