My wife just completed an assignment on the east coast that allowed us to spend several weekends in New York City. We developed a routine that we think maximized our enhanced tourist status without getting too bogged down anywhere. I think our situation is similar to yours.
Many of the suggestions above mirror our experience. We very much like the hop on hop off city bus tours. Sit through the entire tour before getting off. Once you've been through the whole circuit you'll know what you want to see first and you'll use your time much more efficiently. The bus tour is a good first day. We also like the Intrepid and the boat tour that goes with it as a package. You need to do at least one harbor tour. There are almost no real Jewish Delicatessens in New York anymore. There are delis all over the place that sell mass produced bagels and the same Boar's Head brand meets that you can get at your local grocery store. As far as I know, only Katz Deli remains. That is also the deli where Meg Ryan faked an orgasm over her salad in the scene from When Harry Met Sally.
A great walking day and one of my favorites, is to start at the Metropolitan Museum of Art. Walk through the exhibits until you're tired of art. Have lunch in their main dining room. There isn't much to chose from in the neighborhood other than one organic coffee/sandwich shop a couple of blocks away. It's fine, but the hot chicken sandwich in the museum is remarkable. It was a little pricey, but well worth it and the setting is beautiful. Once you're done with the museum, walk out the back door into Central Park. Walk down the Park and stop at the Frick Museum
https://www.frick.org/ at 70th and 5th Avenue. Tour the Frick and go back into the park. Continue to walk down toward West 57th Street. Walk around Columbus Circle and stop at the Plaza Hotel. Go inside and downstairs you'll find a little indoor mall with coffee shops, bakeries, restaurants, and little shops. Have a coffee and chocolate croissant. Then get back on 5th Avenue and keep walking south toward Rockefeller Square. Window shop your way down 5th Avenue. You'll pass the Museum of Modern Art if that's your thing and you aren't museumed out. Keep walking to Rockefeller Square. You'll see Radio City Music Hall, the NBC Studios, Top of the Rock, etc. If you time it right you'll arrive during happy hour at Bill's Burger Bar.
Hours and Locations - Billā€™s Bar & Burger Restaurants Their prices are usually pretty steep, considering it's a hangout for Wall Street types, but the happy hour menu is one of New York's greatest secrets. Draft beer is half off and their Mini B's sliders are five bucks. I think they're usually $15. They are worth the walk just to get them.
By now you're tired, so spend the rest of happy hour at Bill's, maybe take in a tour of Top of the Rock, see the rest of Rockefeller Plaza and head back to the hotel to rest a bit and get ready to go out for a late dinner somewhere special.
That's my favorite day in New York. I've done it a couple of times, and now my wife and son both want to repeat the day every time we're in the City.