There are a number of frameworks for the measurement of sustainability. However, given that you are seeking for instruments specifically designed for measuring the sustainability criteria or ‘outcomes’ post construction, I would suggest the following although mostly related to infrastructure, still provides some directions of a good review of existing frameworks:
Ugwu, O.O. and Haupt, T.C. (2005) "Key performance indicators for infrastructure sustainability – a comparative study between Hong Kong and South Africa", Journal of Engineering, Design and Technology, Vol. 3 Iss: 1, pp.30 – 43.
Another good sources of literature and directions is as follows:
Zhou, L., Keivani, R. and Kurul, E. (2013) "Sustainability performance measurement framework for PFI projects in the UK", Journal of Financial Management of Property and Construction, Vol. 18 Iss: 3, pp.232 - 250.
The following book chapter also provides some examples of existing sustainability frameworks:
Zuo, J., Wilson, L., Zillante, G., and Pullen, S., and Chileshe, N. (2013) Appraising corporate sustainability of construction contractors: concepts and approaches. In Sustainable Business- Theory and Practice of Business under Sustainability Principles (Editor: Wells, G.), Cheltenham, UK and Northampton, MA, USA: Edward Elgar Publishing Limited, ISBN: 978-1-78100-185-1 (HB), pp. 233-247 [Copy Attached].
Some work associated with the testing of sustainability within the ‘housing’ sector, and more specifically on residential development was also undertaken (see Pullen et al. 2010) as follows:
Pullen, S., Arman, M., Zillante, G. Zuo, J., Chileshe, N. and Wilson L. (2010) Developing an assessment framework for affordable and sustainable housing, Australasian Journal of Construction Economics and Building, 10(1/2), 46-64. [See Copy Attached]
I have attached two of the cited publications for your benefit.
It might be a longshot, but one of my former colleagues, Russell James, has an article that might be of interest to you on this front. It is called "Impact of Subsidized Rental Housing Characteristics on Metropolitan Residential Satisfaction", and it is located in the Journal of Urban Planning and Development (2008).
Although it is not germane only to public housing, you might also want to check out my article on "The Greening of the Multifamily Residential Sector"....you can find it on my profile.