I did some research in my game, and it seems that the garbage dump removes garbage evenly throughout the entire blue area covered by the dump.
You can figure this out by comparing
coverage area vs
First note my city's pollution, and the newly constructed garbage dump circled in green.
Now see the dump's coverage:
Now finally if you compare
predicted pollution, you can see that the area covered by the dump gets its garbage reduced pretty much uniformly throughout the area. If the effectiveness of the dump fell off with distance, then around the edges of the coverage there would be almost no noticable effect, however you see a very stark difference between the areas just inside the coverage versus those outside.
So it would seem the best strategy would be to put the dump as far out as possible, while still overlapping the worst parts of your city. By counting the squares it looks like it has an effective radius of about 35.