I work on the University, and there I recovered wired internet rather quickly probably due to backup generators. At home most routers stopped, some even took until the next day to be functional again.

As for mobile connectivity, the main issue was the congestion. The cell network didn't fail, usually, but in most places either your phone wasn't able to connect or had no internet. Too many people trying at the same time, I guess. On the University on the other hand it worked perfectly. Maybe because it's a usual crowded place and there are more resources, but I think it was also because a lot of students (even teachers) went home, so those who stayed were mostly alone with a good internet...but less people to talk to.