I am trying to perform spatial analysis regarding affordable housing across North American cities.
Does anyone know of a source (city, commercial, or other website) which offers real estate or housing appraisal data?
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Affordable housing is difficult to track as there are intricacies to the process: Is it Housing Choice Voucher Program (Previously Section 8), is it a an established property that specifically handles affordable housing (which the government pays a private enterprise to operate), or is it public housing.
You should look at property appraiser data for each county to figure out what basic values are available, then identify where the affordable housing locations are.
Statewide Parcel Data in Shapefile Formats with Property Appraiser Data:
Use Trevor's answer for non-commercial purposes only, Scrapy, is your scraping buddy.
If you adhere to the guidelines, you can access MLS data through the Zillow API.
Finally, you are going to need to go the HUD website to identify affordable housing locations.