For Manhattan, I recommend Bagels & Co (Amsterdam Avenue between 78th and 79th). Kosher bagel shop, very popular with the synagogue goers. Closed on Saturdays. Go early.
There's so much to see in New York City, so hard to advise. Personally, I'd spend less time in the Times Square area. Perhaps just a quick walk through. The 9/11 memorial is something that stays with you, if you want something a bit more introspective.
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