Is vegetarian food served here ?

yes

Yes,and many other Restaurants within a short walk.

Yes, and it is very good. Available in the Greek restaurant off the lobby.

There's a Greek restaurant in the hotel, so I guess the answer is yes

NYC restaurants are inspected and rated by the Department of Health and it mandatory to display the rating in their window. Personally I would not eat anywhere with less than an A rating.

There are Greek and American restaurants at the hotel that can accommodate you and if you're not loving their options the Metro cafe is just 3 or 4 doors North and had a fantastic menu

There is a Greek restaurant attached to the hotel that has a number of vegetarian options. Didn't eat there though.