I've never seen that much aerial traffic over the Hudson as today. All layers of airspace were packed with fixed wings, rotaries and UFOs. Excellent weather everybody was in the air. Saw nice RV10 over VZ, heard him earlier. No chance of taking a good picture today this was a shot in the blind. 125 years young and still going strong.
No special permission needed. For Hudson helicopters are below 1,000', fix wings doing 1,000' to 1,300' (East River below 1,100'). To circle the Lady, you need to go below 500' and keep the 2,000' horizontal separation. The 500' is due to the Newark airspace. If you want to cross central park, then, give La Guardia tower a call. I would not fly up East River unless I have clearance to cross Central Park. You do need a copy of NY TAC chart with you. I find helicopter route chart helpful since it tells me what helicopters are doing. Skyvector has all the charts for your planning. The Helicopter Insert is especially helpful. As Vlad said there are a lot of traffic, especially around the Lady.
