Couple of safety tips: 1) don't leave road maps in plain site when parked at grocery stores, motels, etc. (you want to look like a local -- even if your license plate is not local). 2) Don't stand on street corners with befuddled looks, staring at guide-books.
Maybe I've been lucky? I do both of these all the time. No problems yet. In fact, I often strike up a good conversation because of it. Someone will help me figure out which way I wanna walk and usually throw in a few good tips about things to see and do in their town, or see the maps and ask me where I'm from and where I'm going. Innocent, nice chit-chat.

It makes me sad that people are scared to travel for fear of the unknown. I figure most people feel pretty safe in their home town. Remember that, wherever you go, it's someone else's home town. Yeah, there are certain neighborhoods in some of the major cities that are best avoided but, over all, people are the same everywhere. Just keep your personal safety radar turned on and use common-sense and you should be fine. Basically, the same as you would use in your own home town but maybe turned up just one more notch or so due to the unfamiliar surroundings. That should suffice.

My parents have done a lot of foreign travel. In their late 70s and early 80s, they were wandering the streets of Saigon in Vietnam, the backroads of Turkey, the townships of South Africa, etc. and they never encountered any problems. I would think America would be at least as safe, if not a lot safer, than most of these places. And I think the world is a safer place than the evening news might want us to believe. Remember, they get ratings from the shock value.