Manhattan visit planning - Phase I

My first post on the Manhattan board, how exciting!

My daughter and I will be paying our second visit to Manhattan in August. We will arrive on Sunday afternoon and leave late Friday afternoon. We are staying in the Theater District. Our plans include the MET, the MOMA, the Tenement Museum, and Central Park. We also will do the on-off sightseeing bus tour of Brooklyn (I will post on outer boroughs board). I'm also setting aside time to explore Greenwich Village.

In my first phase of planning, I am selecting all the categories of restaurants I would like to try. I have already selected these categories: dim sum, pizza, traditional Jewish deli, southern Italian, northern Italian, Japanese noodles, and Czech. We want to do a mix of restaurants, markets/bakeries, and food trucks. My daughter is especially interested in a lobster food truck. I haven't figured out a food budget yet, but $80-100 average per day is in the ballpark.

So, my question at this phase of planning is: What other categories should I consider? The variety of food experiences in NYC is so dizzying, it's difficult to plan a strategy for getting the most out of our food stops.

EDIT: I've provided more info on budget, locations, and other details in other posts.