Bushwick wins! At least according to this interactive map on Gothamist detailing the number of 311 calls made complaining of rats. There were a whopping 965 complaints of rat sightings in Bushwick in 2012 – the most reported in ANY neighborhood in all five boroughs. Williamsburg has about the same number of sightings (813) if you combine its 11211 and 11206 zips.
The Upper West Side, a neighborhood with no shortage of rodents, made plenty of noise, lodging around 1,000 complaints from 2010-2012. Residents of North Brooklyn also alerted the city about their own rat scourge, with Williamsburg and Bushwick each placing 800-900 calls to 311.