$500 a month will get you a room share in SF. Even SRO hotels are about $200 per week. Your best bet to find housing will be the shared housing listings on Craigslist.http://www.craigslist.org
You can get $350 for 60 sq ft room, $500 for 100 sq ft room in China town, all utilities included, but you have to share bathroom and kitchen with 30 other tenants.Actually China town is in perfect geography position in SF, you can go everywhere on feet, that is why during last 150 years, white men have tried to drive China town to Hunter point.There are 5 China towns in SF now, most people refer original China town in Grant, Stockton Street.
For that kind of money, it would be best for you to rent a place by the week or month. Look on craigslist for short term rentals.