Visiting from the West
Looking for the best of the basics... pizza, knishes, jewish deli/bakery, italian deli/bakery, bagels. Parents raised in the Bronx moved to CA 40+ yrs ago, used to visit family in NY a lot and enjoy these tasty snacks but been 10+ yrs since in NY. Will be staying upper midtown, and scouring the city (or boroughs?) for a good slice, etc. Recommendations....
Definitely Katz's (for pastrami on rye specifically). The knishes at Zabar's are quite good, though it's a market, not a restaurant, so you need to find a place to eat them. Also on the UWS, there's Barney Greengrass for smoked fish and things like that.
Bagels are more subjective, though when I compare something like H&H to the bagels available elsewhere (the rock-hard banana nut "bagels" they sold in DC when I was in college, for example) I remember how good we have it. Maybe it's best to just try them all!
please try joe's on carmine street for a perfect ny slice of pizza. thin, crunchy crust, but not too thin, fresh, delish sauce with right amount of sweetness, and perfect amalgamation of all the ingredients. i am getting hungry speaking of this. a little known thing about pizza in manhattan by out of towners is that we have a lot of crappy pizza. i am not suggesting in any way that the great is not great. but many pizza-makers fall short in finding the formula of fresh ingredients and not glopping on heavy cheese and toppings to mask the product... ok i'm off pizza soap box . have fun !!!
I resisted mentioning this earlier, since it's an outer boroughs answer on the manhattan board, but if you're serious about scouring the city, I'd get back to your Bronx roots and head to Arthur Ave. Top notch Italian bakeries and delis there, to be sure. DiFara is the best pizza, but it's closed right now (they've been "opening any day" for some time); check the status on the outer boroughs thread. In Manhattan, I'd head up to Patsy's in East Harlem for the best pizza, but Grimaldi's is probably less remote even if it is in Brooklyn, and I prefer Grimaldi's.
I'd listen to RGR about the Jewish food, although I personally think a still-warm plain bagel fresh from H&H is very tasty.
While I agree that "New York, New York, it's a wonderful town..." I don't think there are many excellent Jewish or Jewish-style delis, which are the ones I'm most familiar with. You might be right about Italian delis, but I don't know enough about them to comment. As regards bagels, the only bagel I've tried is from H&H and, frankly, I think they're mediocre.
For Jewish-style deli (not kosher), it's Katz's, where it's all about the pastrami.
My favorite artisanal bakery is Amy's.
For knishes, Yonah Schimmel, though they can be hit or miss.
I have no bagel favorite, but for bialys, it's the one and only Kossar's.
For other borough recs, if you haven't already done so, post on the Outer Boroughs board. But I'll start you off with these. In Brooklyn, for pizza by the slice or by the pie, definitely Di Fara's, and for Jewish deli (kosher), the Mill Basin Deli is tops!
Enjoy your visit to NYC and Bon Appetit!