If you were taking someone who had never been to NYC before to get a slice and a chopped cheese, where would you take them? Has to be Manhattan, no time to make it further afield.
do you care about the neighborhoods you'd travel to to get to these places?
hajji's (blue sky deli) is the originator of the chopped cheese. if there was one place to go for that, i'd go there
as far as pizza goes, there are too many good spots to choose from to be honest. just pick a good spot. the last pizza i had in NY was on a date in manhattan at john's of bleeker street, and it was very good (this was a couple of years ago after the pandemic).
i've always liked patsy's pizza, and the bonus is that it's close to blue sky deli, but both are in east harlem, so take that for what you will lol
since i don't frequent NY anymore since i've been away so long, i'd probably go with somebody else's advice for the pizza