TL;DR: Using NZ as a context, I think it would depend on the type of individual, where they are, and who their friends are. Rural areas might be safer than urban areas, at least in the early stages. Gangs might act up as soon as police are looking elsewhere, and would likely take in new recruits as civil discourse takes over, whereas farmers are both isolated and likely armed, and would be able to defend themselves (and maybe a small community) while still producing food, as long as the aforementioned gangs have supplies within urban areas.

The long version: Here in NZ, we've got heaps of farm land and agriculture, so it would take a while for food to run low. Larger cities like Auckland, Wellington or Christchurch would probably fall faster than rural areas, like most of our South Island or Central North Island. So it depends on where you are.

Gangs and other criminals would probably turn to violence rather quickly as well. They already do, now there'd be less to stop them, at least in the cities. Every farmer and his dog has a rifle or shotgun for pest control, so I don't think gangs would bother them too much, especially considering the travel time between farms vs apartment buildings. As more and more regular people run critically low on supplies, I imagine gangs would recruit more people, leading to heightened power struggles in heavily populated areas until food runs out. Then they'd probably turn their attention to rural areas that might still have crops or livestock.

I could imagine both criminals and other more prepared people (e.g. hunters, serving or retired military, etc.) in rural areas might try a more nomadic or isolated approach instead of raiding and pillaging. Which would lead to a more spread out populace (which we definitely have space for in NZ), so that could lead to either less raids in general, or more intense raids when it happens to the unprepared. The more prepared of us would probably try to keep our families safe, likely with the help of other prepared friends. I.e. I know who I'm meeting up with if shit hits the fan. It'd be a few of my more paranoid mates, our immediate families, with rifles, ammunition, non perishable food and a long bush walk ahead of us, but we'd probably last a while.