The places you mentioned are some of the trendiest restaurants in the city. Are you looking for a trendy/cool atmosphere or just a solid meal?
For steak, I’d try Wolfgang’s, Gallagher’s (might be tough 2 days out, though), or maybe Catch Steak if you’re looking for trendy. The Grill if it’s in your budget, but it’s very expensive (owned by the same group as Carbone).
For Italian, La Pecora Bianca is a solid choice and you should be able to get a reservation at one of the locations. Bad Roman is very big on social media and has a lot of space; if you can’t get a reservation but are willing to wait (it’s in a mall) then they might seat you. The food is okay but the drinks are really good. I also like the restaurants (any of them) in Eataly. I’d avoid the Flatiron location because it’s chaotic, but FiDi or SoHo might have something.