You can
anchor near the Statue of Liberty - just watch out for the white exclusion zone buoys. Easy to spot on a chart and during the daytime. I'm not intimately familiar with the area, but I do know there's shoaling south-west of the statue in some areas. It's on the
charts.
I do not think you can or should anchor south of the Williamsburg Bridge. Even if technically possible during that time of year (not too close to where they set off the fireworks), that would be pretty wild with tides and traffic.
You can anchor many places in the "Upper Bay," but if you want a significant amount of stress reduction and do not mind being further from the show, consider
anchoring somewhere in the
Raritan bay, a good option is Sandy Hook near the Coast Guard station. It's pretty far but you'll still see the fireworks on a clear night.
NYC harbor gets crowded, especially during that time of year. Maybe not technical
anchorages, but you can also anchor in many places in the
Hudson. Just look at your
charts and be extra mindful: there are a lot of things to consider in this high-traffic area, that should often be more than just a consideration; ferries, tunnels,
cables, obstructions, and tides. Can you anchor above the Lincoln Tunnel? I don't know, I wouldn't!
We have anchored near the GWB before. That will be quieter. We anchored on the north side of the bridge, the west shore of the river, but I think you could anchor on the south side. Again, check your charts!