The description of the effect is actually quite confusing as the internal mechanics don't work the way "nearby" would suggest.
Most buildings within Tropico have two values to determine the range of their modifier: radius and fall-off.
Radius determines the area around the building where the full affect applies. This is an internal number, and it's hard to say how big a circle with a certain radius would look on the map. The best way to get a rough idea is to place a educational facility like a school or college. You'll see a circle drawn around these, in the case of any educational facility this is a radius of 300.
Fall-off is a little different, no circle is drawn around a building for fall off. Fall off basically means that the effect of the building slowly diminishes until it reaches the border of the fall-off. So for example, a building that modifies X for +10 with a fall-off of 100 would modify X +10 in the center, +5 at a radius of 50 and +0 at a radius of 100.
The effect for fire-stations have a radius of 0, and a fall-off of 320. Because there is no radius you don't see the effect clearly on the map.
So too answer your question: nearby means the effect is strong near the building, and diminishes the further away you get. In the case of a fire-station the effect's circle is a bit bigger than that around a educational facility.
A complete list of buildings listing their radius and fall-off for local effects can be found here.