OK. For Massachusetts 2015, to pick a town and a city that each have one high school and are both expensive property values.
Cambridge (expensive city) $27,569 per pupil
Concord (expensive suburb) $17,517 per pupil
http://profiles.doe.mass.edu/state_report/ppx.aspx
Rankings
Cambridge Ringe and Latin was 214 out of 340
Concord Carlisle High was 27 out of 340
https://www.schooldigger.com/go/MA/schoolrank.aspx?level=3
Not cherry-picked data.
A lot of the difference is that cities, even expensive ones, are cities. A lot more diverse student body. A lot more students with problems at home. More disruption, etc. You can spend more money but the average student in the city school almost certainly has less parental involvement and less of a home environment that's conducive to learning than in the tony suburb.
The linked article (and decades of debate) notwithstanding, it's also hard to really correlate spending per pupil with educational outcomes past a certain point--especially as measured on standardized tests.
Poorer cities do spend less. Two Lawrence high schools have the worst test results in Massachusetts. But its spending, $14,475 per pupil, is still only a bit less than Concord.