I recommend starting on at either Altlantic or Passaic, walking slowly, and sampling lots of things along the way. All of the local empanadas are great although I'm partial to the fried cheese empanadas at Galapagos. You will also want to try the jerk chicken at Boomerangs (which is re-opening this week). For desert, try one of the tropical, cold fruit shakes at Bohemia.
Remember- not all food vendors at the festival are local. So if you want "local" make sure you are getting it.
A complete district restaruant guide is here:
http://www.uppermain.org/restaurants.html I eat at just about every restaurant on Main and don't have a bad thing to say about any of them. My regular rotation is Kebab House, Potrero Grill, V&T Salumeria and Tandoori Chef but I switch it up quite a bit. Just outside of the district is Villa de Columbia, on Mercer. Their Friday fish special is a must try.