ooh, you've asked one loaded question.
As a vegetarian who just got back in September, I can recommend a few excellent choices:
Le Cellier. It's a steakhouse, sure. But they have an excellent pepper and polenta dish.
Prime Time Cafe. Stuffed peppers that were so good, I ate the entire meal.
California Grill. Breathtaking view, incredible upscale vegetarian choices.
Jiko. Oh baby, this is vegetarian cuisine with so much flavor.
Tangerine Cafe. A Moroccan lunch. Yummers.
Mama Melrose. Brian the chef cooked me up one fantastic vegan dish with pasta, veggies, and garlic. Holy cow this was my favorite meal of the entire trip. Unfortunately, it wasn't on the menu and they cooked it for me special.
Concourse Steakhouse. Yeah, another steakhouse. But again I had a very good pasta and veggie dish.
Those are the highlight veggie meals from my last trip. I found most restaurants in the World to either a) have vegetarian choices, or b) be extremely accommodating when your tastes didn't match the menu. Enjoy.