American Heritage Dictionary "inner city" as "the usually older, central part of a city, especially when characterized by crowded neighborhoods in which low-income, often minority groups predominate."

In the US, the expression is used specifically in reference to the low economic status of the families living in these areas, and the social problems concomitant with the economic difficulties (drugs, prostitution, AIDS, crime, etc.).

In other words, the point is that these kids are poor.

If your readers are fully familiar with Western urban sociology, then أحياء أواسط المدن may be fair enough. Otherwise, this may be an appropriate exception to the rule of "translate -- do not explain."

You may also think about combining both:

الأحياء الفقيرة بأواسط المدن

If this is a headline, it may be too wordy. Use your judgment.