Does living in a poor neighbourhood affect cognitive function in elderly people? - Yes

Study 1 - American Journal of Public Health

Study size 6000 plus

Older women who live in a lower socioeconomic status neighborhood are more likely to exhibit lower cognitive functioning than women who live in more affluent neighborhoods, according to a new RAND Corporation study.

http://www.sciencedaily.com/releases/2011/08/110802125604.htm

Study 2 - England... Neighborhood Deprivation, Individual Socioeconomic Status, and Cognitive Function in Older People: Analyses from the English Longitudinal Study of Ageing

Study size 7000 plus - English Longitudinal Study of Ageing (ELSA)

After allowing for individual socioeconmic status, elderly people living in poorer neighbourhoods demonstrate lower cognitive function than average.

The characteristics of the places people inhabit influence many aspects of their health and well-being. Living in a deprived neighborhood has been shown to be associated with risky health behaviors,¹ poor cardiovascular health,² higher mortality,³ and greater depression.⁴ Various mechanisms to account for neighborhood effects on health have been proposed, including access to resources such as primary care and stores selling healthy food and relationships with the built environment.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2671806/

The article offers some further reading including

Graffiti, greenery, and obesity in adults: secondary analysis of European cross sectional survey.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1215553/