The cities were largely abandoned, soon after the electricity stopped. The Matheson family was shown walking away from their home, with what they could haul in a child's wagon. As they walked through the streets, they were nearly alone. Almost everyone has fled from the city.
All cities would become uninhabitable, soon after such a disaster. In the immediate aftermath, there would be widespread looting, and other violence. Then there would be shortages of food, medicine and other essentials. Within weeks, disease would spread throughout any areas of concentrated population. People would flee, to escape the violence and disease, and to seek food.
Well-built buildings can last a long time -- if they're occupied and maintained. Deserted buildings soon start to fall into disrepair, and then decay. In the second episode, we see buildings burning, and no fire departments to respond. The fire fighters have probably left -- and even if they were still there, their equipment no longer worked. It's apparent that looters have vandalized many buildings. Vandalized buildings decay rapidly.
We don't need to imagine what happens to unoccupied buildings, that have suffered from vandalism. Just search for photographs of the urban decay in Detroit, over the last couple of decades.