I had trouble exporting data directly from OSM, so followed a link from there to the Overpass API — the only difference I can see so far is that I have to change instances of

Cases[nodeElem, {__, "lat" -> lat_, "lon" -> lon_} -> {lat, lon}

to

Cases[nodeElem, {__, "lat" -> lat_, "lon" -> lon_, __} -> {lat, lon} 

...in order to get the early stages of processing to work the same as the examples. I assume there's just a slight difference in XML structure.

This is super cool!

wow! amazing post! I've wanted to this for a while actually! But based on the new TravelDirections functionality. But this is much more neat. I love how you can see the Manhattan Norm so clear!

ContourPlot[Norm[{x,y},2],{x,-4,4},{y,-4,4},ContourShading->None]
ContourPlot[Norm[{x,y},1],{x,-4,4},{y,-4,4},ContourShading->None]

Would be fun to figure out the 'Norm', the exponent (2 in an open field and 1 in Manhattan and most American cities) can be found for various cities...

Fantastic work!