"Does anyone recommend a place to go in New York?"
There is no such thing as ‘illegal’ in matters of grammatical usage. I should say a more common way of saying it might be
Can anyone recommend a place to go in New York?
But ‘does’ works. Similarly, I might think the sentence unclear as its stands. Does it mean ‘a place to stay, or a place to visit, something else? But unclear sentences are not thereby ungrammatical.
May be you could say ‘a place to go to’. But the ellipse is common enough.