In a futile attempt to put this in perspective I will reference the UCJI for Oregon. That is the Uniform Civil Jury Instructions. This is what is given to the juries at trials so that they understand how the law works and what must be proven. Each state is different but most have to prove the same things as most of this is common law as opposed to statutory.
UCJI 20.01
To recover the plaintiff must prove two things by preponderance (51%) of the evidence: (1) that the defendant (the city) was negligent in at least one of the ways claimed in the complaint; and (2) that the defendant's negligence was a cause of the DAMAGE to the plaintiff.
UCJI 20.02
Common-law Negligence
In deciding whether a party used reasonable care, consider the dangers apparent or reasonable foreseeable when the events occurred. Do not judge the party's conduct in light of subsequent events; instead, consider what the party knew or should have known at the time.
A person is negligent, therefor, when that person does some act that a reasonable careful person would not do, or fails to do something that a reasonably careful person would do under similar circumstances.
UCJI 20.06
Foreseeability
A person is liable only for the reasonably foreseeable consequences of his or her actions. There are two things that must be foreseeable. First, the plaintiff (girl) must be within the general class of persons that one reasonably would anticipate might be threatened by the defendant's (city) conduct. Second, the harm suffered must be within the general class of harms that one reasonably would anticipate might result from the defendant's (city) conduct.
UCJI 21.02
COmparitive Fault/negligence
The Plaintiff and the Defendant have each alleged that the damage was caused by the other's fault/negligence. If you find that both the defendant and the plaintiff we at fault/negligent in any respect alleged which was a substantial factor in causing the damage alleged, then you must compare the fault/negligence of the plaintiff to the fault/negligence of the defendant. [In making this comparison, you are to consider the relative unreasonableness of the parties' conduct and not the mere physical causes of damage.]
UCJI 23.02
Causation
A cause is defined as an act or omission that is a substantial factor in bringing about the damage. [A substantial factor is one that is an important or material factor and not one that is insignificant.]
Also please note that American Common Law is based on the reasonable person standard. A reasonable person is one that takes proper but not excessive precautions.
I guess you could say that she was not a reasonable person and that she was at least comparatively negligent if not wholly negligent in her cause of damage. It was not foreseeable to the reasonable person that a citizen would be walking on a city street, not exercising due care, and falling into an open manhole.
A reasonable person would not be walking on a city street without watching where they were headed. Even if she was a minor it matters not to the law. She is still treated the same as another minor would be. If she was in a protected class, blind, having a retardation of some kind, then yes the standard of care by the city is higher due to this knowledge. In other words if you are doing construction near a school for the blind, you better make damn sure that you have every conceivable barrier in place.