Where in New York? Even if in the city (my assumption), that's a lot of ground to cover.
For steaks, Peter Luger (over the Wlmbg. Br) or Sammy's Romanian (which is Romanian/Jewish comfort food but has really good meat and a festive environment). Both will likely need reservations in advance.
For Italian, some of my favorites are: Ecco (Tribeca), Il Melograno in [censored]'s Kitchen, lowest key is the Meatball Shop, which has multiple locations, but I like the one in Chelsea. I also really like Trattoria Dell'Arte, in the Theater District. I heat their food is really good, but what Ive been there for is their great vegetable antipasto table and the braised octopus before or after an event (watch the crowds, others have the same idea)
For French, I like Les Halles in the Financial District.
For low-key Mexican, I like Lupe's East LA Kitchen in Soho.
Black Iron Burger near Penn Station is really good for burgers and beer.
Ive eaten at all these places multiple times. Ive gone to a ton of other places too, but these are my favorite.
If youre not in NYC, but rather out on Long Island, there's great Turkish out around exit 62 on 495. Also in Port Jeff or around there, is a restaurant called Sea Basin, I think their Fra Diablo is some of the best Ive had...