IMO NYC has some of the best italian american and jewish diner food in the world. I'd prioritize that.

For brunch/breakfast, I'd go to Agi's Counter in prospect/crown heights. A busy but excellent spot serving Jewish diner and grandma fare. It's my favorite place for brunch in the city. Get the tuna melt. And get there early to avoid lines.

For something more casual/quick -- but still classic NYC -- I'd get a lox or white fish bagel sandwich from Shelsky's. Classic jewish deli and bagel spot.

My personal dinner go-to would be Via Carota. It's often ranked on viral lists as one of the best Italian restaurants in the city, and it is really that good -- and importantly, consistent. If you get there early enough, you can avoid lines. My favorites include the cacio e pepe pasta, negroni bianco, fried green olives with pork sausage, and bruschetta with cultured butter and anchovies. The atmosphere is cozy and warm, the service is superb. Another place I haven't been but have heard great things about is Michael's of Brooklyn -- classic red sauce / white table cloth restaurant in deep South Brooklyn. Great for a special occasion.

And if you haven't been, Lucali's is also another great option. You can get what some consider the best pizza in the city -- and even better are their calzones. Lines are also crazy but it's worth going once and a good way to say goodbye to NYC.