If you are toting an expensive camera, replace the "brand name" strap with a plain black neoprene one (more comfortable anyway) and cover the logos on the camera with black insulating tape. No point advertising the value of your kit to any ne'er-do-wells that might be hanging about.
For desert safety, a US friend of mine recommends a .38 Special with the chambers loaded, alternately, with solid slug and snake shot. Then, whatever attacks you, you only have to pull the trigger twice.
Having said that, having travelled extensively in USA (44 states at the last count), I have never found well-lit city downtown areas or any rural areas any more threatening than in Europe. It really is about behaving modestly and sensibly.