Some clarifications are in order.
It is true that the Chicago suburbs are characterized by a large number of relatively small schools districts. The borders of these districts generally DO NOT coincide exactly with the towns they serve. The separate taxing authorities in many cases came into existence at different times.
In general the advantage to the system that is common in the Chicago suburbs is that the elected School Board of a district was to be very responsive to the parents that the school district serves as well as respond to spending concerns of the resident property owners within a districts. The last phrase is key and it bears elucidation:
RESIDENT PROPERTY OWNERS are the people that by virtue of living in an area can vote for in the School Board elections and because they are property owners they must PAY PROPERTY TAXES which are the primary means of support for the schools around suburban Chicago. The result of this is that areas with large numbers of non-residential properties can have very well equipped schools at relatively modest cost to the folks that use the schools. Becuase of the way in which property taxes are computed and referendums approved it is entirely possible to have a low tax rate and excellent schools. Similarly, in area where the most expensive homes bear a large burden of the taxes the relative amount that any normal tax payer shoulders is rather modest. The State of Illinos does report on the amount of property wealth each district has per student and the statistics pretty much show that districts that can afford to have lower tax rates per students (due to high property values / large amount of property wealth per student) can afford to spend the most.
HOWEVER the correlation between simple spending and student achievement is NOT BORNE OUT nearly as strongly as the correlation between areas with HIGH INCOMES and high student achievement. Thus the IDEAL school district is one with : Large percentage of high income parents, large amount of valuable real estate and above average proportion of non-residential property.
The first two are far more important than the third.
This explains the results of high achievement and LOW TAXES in districts like Butler 53 which serves portions of Oak Brook and District 103 in Lincolnshire becuase of the relative value of corporate office buildings and retail shopping areas.
The rest of the data can be cross checked via the stellar results of places like District181 which serves Hinsdale and most of Clarendon Hills and a bit of Burr Ridge in the western suburbs, and neighboring District101 in Western Springs. These are the most affluent area along the BNSF rail line where even with very high average home prices there are also a large number of individual homes that are valued at many times the high median prices. A similar situation can be found in PORTIONS of other schools districts and then the concept of "attendance area" is needed to explain how some portions of districts have much better performance than others. Thus large districts like Naperville 203 have some stellar schools and some that are 'merely' far above average.
I strongly recommend following the data from US News that does NOT rely solely one a one dimensional analysis like the weak tests the State of Illinois self administers. Unfortunately USNews does not include elementary schools so one must follow back to the feeder elementary schools and adjust for the weak State Tests which only attempt to set a minimum and thus far too many high performing distances are separated by fraction from 100% mastery and the selective admissions schools of the messed up CPS crowd the top (as would be expected when the admissions process for "gifted & talented" assumes mastery...)
Best High Schools Search - US News and World Report
http://www.chicagotribune.com/media/acrobat/2009-10/50168344.pdf (broken link)