Although i havent any direct experience with a good place in NYC, I might be able to get a recommendation. The place I go in Westchester does an excellent job, but I put lug soles on my shoes, they are softer and offer better grip on NYC sidewalks whereas dainite works better on london cobblestones. A little less hard wearing but the added expense is worth it to avoid slipping and banging the back of your head.
Theres a place like on 8th avenue and 50-51st street that repairs all the shoes for Broadway performers run by some Russian guy. I cant remember the name. There is also a place in Grand Central that does a reputedly good job but again, the actual name eludes me. Maybe someone else can fill in the blanks.