A word or phrase that describes overlooked structures that are part of the fabric of modern living?

A part of what you are referring to goes by the name of infrastructure". This has been mentioned already in this question.

• train stations
• bus terminals

Another goes by the name of street furniture (Wikipedia) (also called "public furniture") or "urban furniture" (What is urban furniture?), but there seems to be yet no very precise assignement of the terms (difference).

• bus stops
• fire hydrants
• street name signs
• newspaper stands/racks
• bike racks

(Wikepedia) Street furniture is a collective term (used in the United Kingdom, Australia and Canada) for objects and pieces of equipment installed along streets and roads for various purposes. It includes benches, traffic barriers, bollards, post boxes, phone boxes, streetlamps, traffic lights, traffic signs, bus stops, tram stops, taxi stands, public lavatories, fountains, watering troughs, memorials, public sculptures, and waste receptacles. [Are also comprised under this heading the following] (Wikepedia)

• Fire hydrants.
• street name signs