Oh the nuke plant won't hurt you - I only throw up 4 times a day, its really not that bad [:-mischievous] ...
South of Rockland the only place I know of would be the Piermont area - but it can get very shallow in there. Further north, there are so many good places once you get past Poughkeepsie. For example, in the vicinity of Norrie Park, either near Esopus Island or on the north side of the park near the Mills mansion. Or you can run up the eastern side of the Mid Hudson Bridge (if you dare) because there's plenty of water there if you know where you're going and follow the chart, and most of the boats will be crowded into the narrow channel on the western side of the River. You can anchor near Athens, north of Catskill on the western side, or Gay's point (eastern side), or Schodack Creek (eastern side - which is now part of a state park I think, but it has no facilities). And of course the three big creeks previously mentioned. I think the one creek everybody forgets about is Saugerties (Esopus), because the facilities are lousy, but once you get inside it looks like a beautiful anchorage area there, and you can explore up to a neat waterfall with your dink...