Hours to Days.
T+ a few seconds; unless all the cities power requirements are met from within itself (unlikely), power dies in many if not most parts of the city. If power IS internally supplied to the city, these same things still happen, just a little slower. The internet dies horribly, as does just about everything long distance that depends on it (modern civilian telecom). Motor traffic comes to a standstill as traffic regulation devices stop working.
T+ Minutes; things will be mostly calm as your individuals stumble around and flick circuit breakers, commiserate with the neighbors about people driving their personal vehicles into telephone poles, and muse that they can’t get anything done at the office. Slowly it will start to sink in that this is not a local thing, or a quick-fix thing. Battery operated devices that connect to satellites and people with functional radios notice they can't contact anyone or anything outside the city; Ex. GPS and HAM radios. Rumors of doom, world war, alien invasion spread from within the city. (per Mindwin suggestion, thanks.)
T+1 hour and people start to die; lack of response of emergency services, hospital patients waiting on the transplant that was en-route, etc. Worse, stories about how the outside-world is just gone start to propagate inwards from the cities edges. People generally aren't panicking yet, but the undercurrent is there.
T+2-6 hours; things start going down hill; any place with food and bottled water is emptying or already empty. Individuals start to panic at this point, not able to charge their purchase to their credit cards as the processing facilities are gone as is the telecom network; theft and small scale looting starts.
T+6-12 hours; looting and riots. People are in full panic mode as stories of the outside world being gone penetrate to a majority of individuals. Food is gone from public stores. Emergency services are totally overwhelmed (being only able to deal with a 5-10% disturbance, a near total disturbance causes them to become totally ineffective.) Someone starts a fire.
T+ 12 hours; Anarchy
T+ 2 Days; people start to starve (just the start of the starvation process; people feeling true hunger for the first time in their life). A modern city only holds a few days of food within itself to support its population, and some wont have any food stores at all. Without massive and constant importing of food from outside mega-industrial-farms, there is simply not enough to sustain the majority of the population. Some individuals and groups realize this and attempt to escape the city by traveling out, looking for a better environment, Meanwhile the City steadily degenerates as people start killing and stealing from each-other more often for basic necessities.
T+ 1 Week; Large amounts of the city's population are dying. Food is gone and people are resorting to any method they can to get more. Increasing numbers are attempting to leave the city for a better place, but the resources on the way have already been consumed by preceding travelers, making it harder for the following ones. The later groups attempting to flee, weak already from starvation, are not able to travel far before they too expire.
T+ 1 Month; the city has turned largely into a ghost town and nature is starting to reclaim areas.
At almost any point you might find survivors (if there are any) from outside the city trying to make their way into or towards it, especially in the first few hours, but the numbers of individuals able to actually approach and enter the city are going to be so low as to be insignificant.
TLDR; Food and water run out quickly, It's doomed.
