There is a creek 5 mins from my house. I fish the upper reaches a lot - its 20 miles away to the good water that is,similar to the pix David posted. Where it runs near my house it has slowed down and warmed up and picked up a lot of agricultural pollution so it is anything but pristine. There are occasionally good fish to be had though - sometimes smallmouth, sometimes squawfish, sometimes trout.
When I lived in the town of Tigard I was ten minutes drive from a good medium sized river that had lots of public access points and a couple gems of tiny creeks filled with trout or bass.
There are literally dozens of urban credks around here - I try to fish at least a few each year. Some get steelhead and salmon spawners too but you cannot target those species that far upstream.
Some of these creeks get surprisingly wide and deep in places too - one city park has a middling little creek in it that hosts 10 species of gamefish but not in great numbers - but one stretch gets 20+ feet across and deeper than my nipples - I am 6'4" to give an idea of depth. That stretch is lined on both sides with a wall of thick brush and trees and wading is the only way to access it. Fishing is way better in that stretch
I have heard urban streams like this affectionately called brown lines. If the water is not so polluted as to be flamable or corrosive - they ususlly have fish.