I just crunched the numbers on the last two years of closed listings in New Canaan. 

I sorted the list by school zone: East, South and West
Fascinating spreadsheet.
South East West
Original Asking $1,571,742. $1,861,635 $2,350,986.
Final Asking $1,543,084. $1,784,402 $2,265,602.
Sold Price  $1,489,605. $1,702,498 $2,129,125.
Percentage of Orig   94.77% 91.45% 90.56%
Avg. Town Hall Feet 3872 4248 4143
Price Per Foot $384. $400. $513.
The West side commands a higher average price-per-foot than the other two neighborhoods.
South side has slightly smaller houses on smaller lots. This could account for some of the difference.
This spreadsheet is 520 sales between Sept 17, 2012 and Sept 17, 2014.
I was thinking of looking at the average age of houses in each neighborhood.
Perhaps a higher price per foot can be attributed to more recent construction in the West school neighborhood.
In the East, 172 sales, the average age is 1957.
In the South, 159 sales, the average age is 1962.
In the West, 186 sales, the average age is 1967.
(three sales were labelled “other”)
House Sales by Neighborhood