@MarkGossage is absolutely correct. There are a number of delicious steak houses in New York but expect to pay $300 or more for 2 for dinner easily
There are old fashioned diners that serve breakfast all day. I am sure if you google.
Its the same as any place else really, plain meat, seafood in butter is always an option. Tell them you cannot eat gluten so please do not add flour to your food, substitute broccoli for the potato. As long as you avoid chinese food and pizza (both of which are amazing in New York depending on where you go) you will have what to eat. It is one of the restaurant capitals of the world.
If you need to stock up while there, in terms of supermarkets most have whole food and organic options. Trader Joe’s and Fairway are especially good options if you want to buy some cheese or nuts. Zabars is an experience in terms of their cheese and specialty foods although I have not been in years. If you get desperate, which I doubt you will, you can always buy a bag of peeled eggs to eat on the run