there are a few established squats in the city that occasionally house kids just passing through, but there are TONS of houses you could just squat in. i don't know what part of the city you are in, but theres a pink house on touro that i know is open.
or you could go find a relief group that will feel/house you for free if you do some work for them. common ground is one, commongroundrelief.org, you just go down claiborne till you cross the industrial canal and then take the first left and then the next left and your there. or emergency communities, i don't know their website, they're pretty far down on st. claude, also across the industrial canal. EC also serves 3 free meals a day.
have you been to ironrail yet? people there could probably help you out.
and a church serves free meals friday, saturday, and sunday right outside the quarter. walk down decatur till you hit elysian fields and theres a parking lot there, they serve at 7pm if i remember correctly.
and cafe du monde never cared if i table surfed.
i hope that was helpful!