You can make a quick illustration from a portrait in very easy way.
I recommend to work with a big canvas and high resolution (7000px and 300ppp). We’ll use a white layer in the bottom and 10 pixels black wide Brush Tool.
With Photoshop, create the outline with the Pen Tool (P) and stroking the path with the Brush Tool, trying to make it as close as you can. Several layers can be used, where you can paint one over another and erase without messing up with other layers. It’s nice if you group the layers in folders.
Once you are finished with the outline, group all the layers (Ctrl+Shift+E/Command+Shift+E) export the file in TIFF format descarting the layers and with LZW compression.
Now in Illustration, we open the file and use the Live Trace Tool with the default options in Comic mode. You can play with this options if you want something different.
Once traced, we expand and ungroup everything. Now we can group the parts we want to have the same color (Ctrl+G/Command+G) and the assign them a color for the path and the fill.