Every month, city planners come to East New York to explain how the city wants to help this corner of Brooklyn, scarred by decades of poverty and violent crime, grow. They will invite developers to build up local streets in exchange for more units of affordable housing. They will invest in new trees and sidewalks. Better services and shops will follow, they say.

And every month, the grumbling ensues.

“We see what’s going on around in the city,” said Joyce Scott-Brayboy, 58, a local community board member and retired city worker. “No to that in East New York. No. No.”

Hers is the first neighborhood Mayor Bill de Blasio’s administration has chosen to focus on under his affordable housing strategy, one of his chief policy initiatives, which he made the centerpiece of his State of the City address on Tuesday.

Ms. Scott-Brayboy is hardly alone in challenging his vision. Around New York, people who have watched luxury buildings and wealthy newcomers remake their streets are balking at the growth Mr. de Blasio envisions, saying the influx of market-rate apartments called for in the city’s plans could gut neighborhoods, not preserve them.