I've seen people speaking all the time in New York City parks for  a variety of reasons, exercising their freedom of expression such as dance or music in Central Park. For many years I lived right next to the 72nd Street Concourse  and you'd see  a jazz band play regularly at the entrance to the crossing (west side across from the Dakota) and dancers, drummers and others would congregate at Bethesda Fountain. And you'd also have your host of speakers there too who might talk about issues relating to politics, local city and resident concerns, etc. You can choose to speak and, if people want to listen, good for you.

If you're expecting a larger group, you should obviously not  set up near the roadways where increasing numbers of people could create an issue. Better to do so in areas such as the Naumberg Bandshell, where there is much more open space. I'm unaware of any law that prevents you from expressing yourself and having people randomly deciding to stay and listen to what you have to say.

If you're talking about a planned peaceful assembly outdoors, you may want to look at the New York City Parks  Department General Provisions Section 1-03.   If you're planning an event in a New York City park, such as an outdoor birthday party with 20 or more people present, the New York City Parks Department actually requires a permit to be filed. There is also a New York City parks special event frequently asked questions page which is similar. I've never heard of anyone actually applying for small parties or events or having it being enforced - but it could be as those are the park regulations. There may be others of which I am personally not familiar.

For a place of assembly (which is can be an outdoor area that is adjacent to a building but not necessary in a park but on a roof, outdoor area for a restaurant, etc.),  the New York City department of buildings may govern and has a place of assembly guide.