Great question! Quito is kind of shaped like a straw, long and narrow. You can actually see from one side of the city to the other along the width, but to go from the northern end of the city to the southern end can take an hour or two (especially during rush hour)!
I’d recommend foreigners to live around or near the Carolina Park/ QuiCentro Shopping area in the north of the city, just south of the airport. I don’t recommend living in the bohemian backpacker area “El Mariscal” because although beautiful during the day, at night it can be a bit rough around the edges. That also goes for the colonial “el centro” area.
I don’t recommend living very high up the hillsides because the public transport doesn’t go there, you will need a car.
And I don’t recommend living in the valleys around Quito unless you like peace and quiet, I prefer city life.
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