Any ideas how to start making a customized city map (one example below). I'm fairly good in using Illustrator and Inkscape but I'm unsure what an optimal workflow would be.
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The easiest way:
If you want to do this in a much faster way you could go to http://www.openstreetmap.org/ and find a street map you want your map to look like. Then click 'export' and download the map as pdf (Map will be vector) which you can open in Illustrator and modify it to match your needs.
If you want to do it from scratch:
If you'd rather start from scratch, you're talking about cartography with the difficult fact-finding and accuracy stuff cut out. It's not half as daunting a task as it initially looks - the key is in the preparation.
Broadly speaking, a typical cartography workflow (minus the research and geolocation) is:
Everything in a map signifies a type (and usually also, subtype) of thing, and everything about a town or city has a reason for being where it is. Maps look daunting to create, but when you pare it down to a palette appropriate for the detail you want to focus on, and when you progressively build up the town from a logical starting point, it's not that daunting.
You can download a free map from a site I built: http://openvectormaps.com. All the maps are in vector format and you can construe it to your liking.