people survive here for bare minimum at around $2k/m
1bdr apt = $1k+/m outside of Manhattan; subway/bus $2 one ride, $10 lunch
grocery is not that high up in price than rest of the country.
for 20k/y you might have some moneys left for books and beer.
i remember living in brooklyn 8-9 ago on a very limited money during my dark ages, i would spend $20/week on food that's it. i survived
living in the city w/o good financial backing is crazy, i remember looking at aptartments in the sity, 500 sq.f studio would run for $1.5k+ - some peoples closets are larger than that. I was back in 2000. I ended up with huge 1 bedroom apartment in brooklyn sheepsheadbay area for less than 1k at that time.
the city is divere so you might find lots of different options.