I feel your pain. Eating out is the main way that people socialise here in Kuwait (no pubs and not much else to do!), and if I don’t eat out occasionally I don’t get to see my friends.
With a lot of perusal of restaurant menus, and a bit of experimenting, I’ve found I can actually get away with eating in a few places. Any French-ish restaurant that serves omelettes is good – I ask them to leave off the bread and any salad dressing. There are also lots of Lebanese and Iranian restaurants here, and from their menus I can eat: shish tawouk (grilled chicken with a spice mixture on it), baba ganoush or mutabal (both aubergine-based dips – not everyone can tolerate aubergine though), any kind of grilled chicken or fish, and any salad without dressing. They also usually serve fresh lemonade with mint, which is literally lemon juice, water, mint and sugar, and as it’s made fresh I tell them to leave out the sugar.
Perhaps you could look around for those kinds of restaurants and experiment with a different kind of cuisine for a change? I wouldn’t recommend the pizza/bagel route. The only time I (inadvertently) ate something with sugar in it, after about a month on the diet, I felt awful for a week after. I’d stick with the food restrictions and enjoy your trip to New York, personally!