Is $1,000 a week after taxes enough to live in San Francisco or Oakland ?

Most expensive and pathetic cities in America!

Easily, if you start with an SRO, they were going between $250-$350 per week even before COVID in San Francisco. Shared bathroom, but a roof over your head. Just stay out of the Tenderloin, it's an infested jungle. This would give you enough time to start shopping for a studio.

Oakland yes ,  SF , not a chance unless you sleep in your car .

Oakland has a very high crime rate , so you have to be very careful

where you move .

$1000/week in San Francisco you will either need a roommate or start eating a lot of macaroni and cheese. 

After taxes you'll live pretty well, actually.

Oakland is a bit cheaper, but there are suburbs in the area that would be cheaper still.  The average studio in Oakland rents for about $1300-1500 a month, while the average studio in San Francisco rents for about $2200-2400 a month.  I'd say you might be able to swing it, but it will be tight depending on your other expenses.

Oakland is cheaper than San Francisco.  But Oakland is not a -suburb-, it's a city in itself.  There are suburbs that are cheaper fairly close-in.

Check Craigslist to see what studio apartments go for.  They're going to be cheaper on the Oakland side of the bay (the East Bay).

Yes it is. I make less than that and live in San Francisco. Oakland is more cost effective. You can rent a small studio apartment for under $1000 there. 

Earning $12000 a year would make your rent allowance about $333.33 a month.

I don't even think even in the most boon docks of boon docks you will be able to live anywhere in the California on that income.

With minimum wage in California of $14 an hour, that's only working 20 hours a week.

Oakland, in the suburbs, you should be able to survive.