Where and how can I legally picket in NYC?

I would go there and ask the cops.

In my experience, the people on the ground may not have the answers,but they can put you on the trail.

You have a right to peaceably assemble. It’s a public square. Picket your heart out. Just don’t obstruct traffic.

I think you might need to get a permit from the city first.

You can picket anywhere you like until someone complains, and you can keep on doing it until the cops show up. If the cops tell you to stop, you should comply- unless getting arrested is part of your plan, as happens sometimes. Remember that the police can arrest you at any time for any reason or no reason- it’s easy for the DA to come up with something to charge you with, and if they let you go they usually don’t even have to worry about charging you with a crime.
If you seriously intend to do this I strongly recommend you don’t go alone. One guy picketing is just a sad, pathetic kook. Before you start, make contact with an organization like the ACLU or another such organization sympathetic to your views which has legal representation. Find one with a branch that is local to you, or rather local to where you intend to have your protest. They or their lawyers can explain the legalities to you much better than Fluther or any other internet community can- and they might even defend you if you are arrested.

Anywhere in the open, you can picket.

I was involved in a picket once. It was amazing how people would scream, “We sre calling the police!”
Our response was “Go right ahead!”
Our rights to picket, free speech, to peaceably assemble are what America is all about. We Americans don’t exercise these rights enough, and they are the rights our forefathers bled and died for.
The police drove by and smiled and gave us the thumbs up.
It makes me sad. These are the rights that make America great.

I should have said that what makes me sad is that people are not aware of, or exercise their rights.

If the Westboro Baptist Church can do it, you can do it. I’m pretty sure your first amendment guarantees you this freedom.