The American Community Survey is an important part of what the US census does. This survey tracked patterns of broadband Internet adoption (which was defined as anything faster than dial up). The results show that poor urban core neighborhoods have similar low levels of adoption as most rural communities.
ACS blog post: https://www.census.gov/library/stories/2018/12/rural-and-lower-income-counties-lag-nation-internet-subscription.html?eml=gd&utm_campaign=20181206msacos2ccstors&utm_medium=email&utm_source=govdelivery
Overall ACS report: https://www.census.gov/newsroom/press-releases/2018/2013-2017-acs-5year.html
ACS blog post: https://www.census.gov/library/stories/2018/12/rural-and-lower-income-counties-lag-nation-internet-subscription.html?eml=gd&utm_campaign=20181206msacos2ccstors&utm_medium=email&utm_source=govdelivery
Overall ACS report: https://www.census.gov/newsroom/press-releases/2018/2013-2017-acs-5year.html