Ditch the white shoes! Minimize staring at maps on sidewalks, and if you need a bit of time to regroup dive into a cafe or kebab/taco joint. If your random track gets you to a sketchy zone, increase your speed and outward sense of purpose.

I have wandered all over a bunch of Mexican cities, and still have only ever been mugged on a hiking trail in the N. Georgia (US) mountains.

Or get a blending in item, like a bag from a cheap local supermarket. Also doubles as my camera bag if I feel I wondered into the wrong place.

Hilarious! You must have only been in the first world then.

I moved from one of the most dangerous cities in the world to one of the safest. Wandering in the latter is fun, in the former - it's Russian roulette. You have to go from A to B, as fast and carefully as possible.