"They" say people in New York City talk fast. That's not precisely true. It's not really talking fast, it's running things together, with no attention to distinct syllables, let alone accented syllables. That has the effect of speeding it up because it shortens it, but it's not the same thing.
The Nugget was hugging a doll when The Man was here, and he said to her, "Gimilmo. Gimilmo." She stared at him, confused. It took me a few seconds to figure out that he wanted her to give him the doll she was holding, an Elmo muppet. I said, "Show the man Elmo", and she give him the muppet. He hugged it properly and gave it back, and she fell in love with him.
Mostly he doesn't do that NYC-speak, except when he makes some offhand remark, and then I flat out don't understand him. He says, "Yeah, I mutter". I used to ask, but now if I don't catch it, I just let it go. If it's important, he slows down and says individual words.
I mentioned the Nugget's confusion to Daughter, and she said that yeah, since she's been talking to the Nugget, she's much more conscious of how fast she talks, how she's slowed down now and doesn't run things together when she talks to the baby. But she still gets frustrated by how non-NYC/NJ people (like ME!) talk so slowly. She wants to shake us, "Come on! Get it OUT already!"
She and I both get frustrated when we talk on the phone. I have to ask her to repeat every other phrase. "Slow down, please." She says she understands a bit better now, and almost apologized for accusing me multiple times of going deaf.