I have worked in midtown and down town Manhattan since the late 80s, so I have put some thought into a scenario such as this. I experienced the power outage in 1996 (IIRC), 9-11 and Sandy. Here are a few of my observations on each of those.

Power outage: Traffic gridlocked in about 20-30 minutes. I was on 46th Street, near Times Square. No cops directing traffic. Probably busy elsewhere. (but some homeless guys started directing traffic in areas and did a passable job). Port Authority bus terminal canceled all buses out within 30 minutes of lights out. Most skyscrapers have some backup power. At least enough to keep one or two elevators operating. Some had full power for lights, AC, etc. Very few New Yorkers carry flashlights. Traffic coming into the city was forbidden for a time.

9-11: I was 50 miles north of the city. About four hours after the second tower went down, I was called to active duty by my Reserve Unit and told to report to South Street, a stone's throw from the towers. FDR Drive and West Side Highway were both shut down. By National Guard. With Humvees and crew-served weapons. Heavily armed NYPD forces were visible too. Canal Street was a dividing line for a while. Nobody was allowed south of there (unless they lived there I think). That was enforced by heavily armed NYPD and National Guard.

Superstorm Sandy: I lived in the city for this one. My ARES (ameteure radio emergency services) group was asked to volunteer to provide communications for the Red Cross. Wind and fire had disables most of the cell towers and public service UHF/VHF repeaters at Breezy Point and some other areas of Queens. We have portable repeaters. NYPD probably does too. Based strictly on my observations in Brooklyn, maybe 10-15 percent of the gas stations had backup generators. Gas distribution became a problem within a day.

Since Sandy, the phone companies have made major improvements in backup power for cell towers. Some have generators, others battery backup. I imagine in the next crisis, cell service will be dependable for 48 hours, then begin to degrade slowly. But in all three of these events, cell service was reduced to texting because of the increased load on the system.

As has been mentioned earlier, the authorities have the capability to shut down cell service to all or parts of the city at will.

I have come to the conclusion that if you are going to bug out of Manhattan, you had better do it at the first sign of trouble. Otherwise, you are pretty much stuck. Trains and buses are out of the question. I don't know how many trains, if any, are diesel powered these days, but signals and switching would be knocked out when the power goes out. Bugging out by car would be a problem if you decide to bug out when everyone else does. You either go early or wait it out. Boat might be doable. I have a sailboat in Brooklyn. I asked the opinion of some NYPD officers I know. They all asked the same question. "How far do you live from your boat?" Five miles as the crow flies. They all gave the same assessment. "It won't be there when you get to the slip."

I suppose your character could keep a small foldable or inflatable boat stashed somewhere and make it across the Hudson to New Jersey. That is the way I would go if I had to bug out of Manhattan. Get across the river ASAP. But you are on foot when you get there. Then you need to get out of Jersey and back to American soil as soon as possible. You can get into PA or upstate from there. Maybe follow the Palisades Parkway north. The Appalachian Trail crosses the Palisades just north of the New Jersey line, and intersects other hiking trails. You may want to get away from the major routes if people are fleeing and fighting over bottles of water and packages of jerky. The population density drops more quickly as you move away from the city if you get across the Hudson. The Yonkers route keeps you in urban territory for too long. And there are some pretty rough neighborhoods there in the best of times. Mount Vernon, Yonkers and a couple of other places are dodgy enough during normal times. Maybe pick Bear Mountain, near West Point, as a rendezvous place. Or farther northeast to Port Jervis. Both are near major transportation routes, but far enough from the city. They are also near large state parks that are undeveloped. Allows you to move, but stay out of sight of the major roads.

Finally. I would stay at the rally point and wait for B. Maybe short, half day forays to better asses the situation and gather intel. But there are too many variables to hope to find her by retracing what you assume her route will be. She may have had to opt for a different route.