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Guess it depends on what you mean by vegetarian. Any kosher dairy restaurant is, by definition, meat-free, and unless you choose a fish dish, the food will be vegetarian. So, of course, there are dozens of vegetarian restaurants in Manhattan.
Go to shamash.com, look at their kosher database, limit yourself to Manhattan and dairy, and see what appeals to you. Only you know where you want to be, how much you want to spend, what kind of food you are looking for, etc.
