Some places I've looked in the past: Crown Heights & Prospect Heights, Flatbush-Ditmars, Prospect-Leffert, Astoria, Sunnyside, Financial District, Ridgewood, Bushwick, "East Williamsburg", LIC, Harlem, Hell's Kitchen, Lower East side (sometimes, though it's also getting some of the most overpriced apartments in the city for what you get).
Please elaborate beyond avoiding trendier neighborhoods.
> Staying away from trendier neighborhoods is my first rule (way overpriced.. and this is what most ppl see first before digging deeper)
Where have you looked?