In NYC subways were halted for sure in the southern part of the city at first the way I remember it. After the first plane hit the conductors were telling people to clear the platforms and trains were carrying people out of the area. I think the entire system went down for several hours? There were electrical problems on some lines and the trains had to work under emergency conditions.
For several days or weeks some of the stations in lower Manhattan were out of service even if they were still in good condition. People could not even walk in lower Manhattan without ID.
The PATH train that runs directly under the Trade Center buildings immediately cleared the station when the first plane hit. Trains with people coming into the station, passengers were told to stay on the train and all people on the platform to get onto the train, and the trains moved out of the area. Path sent in an empty train also if I remember correctly to clear people out. Most likely hundreds of people were saved because decision makers for PATH made excellent decisions. Remember, after the first plane hit, people in the second tower were told to stay put, but the people in charge of PATH took action like more disaster was still possible. The PATH story deserves more recognition.
Ferries also had some changes, but I think they kept running.
Edit: here’s a story about PATH trains. https://www.nj.com/news/2011/08/decisive_action_by_path_employ.html