I'm looking for an intimate restaurant near madison and 45th
I am looking for something intimate, with great food. Gluten free if possible. Good vegetarian options as well.
La Grenouille would be perfect. They have a vegetarian menu too I believe. I assume if you don't eat their wonderful bread, most items on the menu are gluten free? They were closed for the summer so make sure they are open if you are going soon.
It can't compete with La Grenouille, but Madison Bistro (Mad just below 37th) is an intimate room with good food.
The resto across the way at the Morgan Library probably has better food, but it doesn't qualify as intimate in my book -although it's a beautiful room.
(Both are open now, as far as I know.)