Good list all around.
King is great. You could try the original Dante for drinks after, although it'll be crowded. Little Branch is also close, and then just a bit further up you have bars like Pisellino, Katana Kitten, etc. But I've always liked the small bar in the back of the Bowery Hotel, in case going back to your hotel is easier.
For Friday, it isn't on as many lists as some of the other places you mention, but you can usually get a cancellation at Altro Paradiso through resy. It's one of my favorite places, and a 9 minute walk to Comedy Cellar. Penelope's suggestion of Dame is excellent, but I really doubt you would have any luck walking in. I never have.
I'm partial to the Whitney because I'm a member and I think the outdoor stairs give great views of the city, but if you haven't been to MOMA you should go there. The New Museum is relatively near your hotel and also good. All the classic upper east side museums are better if you do Bemelmans, just depends on what art you want to see.
For Via Carota, if you go put your name in at 5:00pm (probably will already be a line outside), you should be able to get a table for 2 around 8:00. They take your phone number and send you a text when the table is ready, and hold for 15 minutes. I know that can be annoying when you are visiting the city. You can also walk across the street and drink at Pisellino.
Pastis is another one of my regulars, but you will need to get a cancellation on resy. No point in walking in.
Another idea is Momofuku Ko, which I think is tremendous and has the benefit of being close to your hotel. The wine director there is a buddy of the mine. She slings some great wine on the tasting menu.
For sushi., you should just do omakase. Shuko and Nakazawa are both kick ass. The former has more of a New York vibe with the music and what not, the latter is like being in Tokyo. Both hit the wallet fucking hard. I'm going to Kosaka tonight to try it out.
All that said, you can change nothing from your itinerary and have a great time. Good work.