The danger of living in an apartment in a utility grid down situation is fire. Your neighbors will be trying to cook and stay warm with grills and bond fires. The fire department will not have the personnel, fuel for the truck or strong city water pressure to put out a fire
On the other hand driving out of the affected area before FEMA and the National Guard have set up gas stations along the evacuation rout is more dangerous. You could break down, run out of gas, be stuck in traffic with other anxious and desperate people.
Instead of abounding the shelter of your apartment right away do three rotating fire watch / trouble shifts. One person has to be awake at all times.
Financial advisers Dave Ramsey and Joshua Sheats will tell you that Apartments are temporary housing until you save up for your down payment on a house.
Pay off all your debts and start saving for a house in a working class neighbor. Fix that house up, flip it and buy one in the suburbs, flip it and buy a house where farm land meets the suburbs.
This way you will have options to dig a well, put up windmills and solar panels and erect a large building with a concrete floor, bathrooms / showers to place travel trailers inside. You can not do that in the city.
You cannot store the gasoline that you will need to drives out of the affected area in an apartment. Try to find a storage unit place that is owned by a prepper who is already planning to have his bug out location there. See if they will allow you to barter work for exchange of renting a storage unit.
Store you water, generator and gasoline on a little trailer inside the unit. Ask if their back up generator is going to be able to open the gate or if he will allow you to install a removable link in the gate chain that you could take apart and reassemble after you manually roll open and close the gate.
Have two ladders to climb over the fence and drop one on the other side and a letter of permission from the owner to show the police.
Also be working on having a reliable, well-maintained mini van with good tires and a hitch to tow the little trailer or pop up camper that you can load up and drive out of the area.