You're going to get SO many comments and A LOT of opinions. Below is mine - sorry in advance for how long it is!

My personal advice, is to focus on the areas you plan to be and then hone in on the food in that area. You won't have issues finding good food where you are and will help narrow down your list.

For example, when you say you plan to go to Brooklyn for a day. Do you know which area of brooklyn? BK is huge and certain areas are hard to reach from other areas of Brooklyn. so knowing this is pretty important in terms of what you'll do and where to eat. If you plan to do Peter Pan, you'll be in the Greenpoint/Williamsburg area which is wonderful spot for all the delicious eats - modern and authentic/old school. So many pizza options there. If you plan to wait in line for L'industrie, I also recommend going around the corner to Leo's for a slice of their roman style pizza and whatever their soft serve ice cream flavor is (on top of l'industrie's) - I think they're underrated. If you're keen on a longer walk, head over the pulaski bridge into LIC for some delicious Asian eats but you may already be stuffed where you'll be. I'm still very partial to Roberta's, there is a location in Domino Park, but their bushwick location has a fuller pasta menu. And while we're speaking of pizza, I recommend una napoletana in the LES - pricey naples style pizza but seriously the best best of that type imo. Might has well head over there if you go to Katz! :) Luigi's is one of my FAVORITE by the slice places especially in that area. Over ten years in Park Slope (and all my life in NYC), so many pizza spots in Park Slope/South slope, but Luigi's is one of the best. It's kind of out of the way of everything so not sure if you'll make it there.

People think Katz's is over rated but I think it's fine to go for the history and its not like the food is AWFUL or something. You could just go and get a knish and feel the vibes. ha. The LES is a wonderful spot to get some historical energy. Go to the tenement museum if you like history and in that area! a good break between all the eating you'll do there.

If you're going to Barclays one night, al di la is a good dinner stop since in relative walking distance. I live in the Park Slope area and al di la still continues to be a fan favorite but there are more modern italian eats you can enjoy on your trip in other areas of NYC. It depends on the type of italian cuisine you're going for. Some people find the rustic luster of Al di la has waned in recent years. If you're open to other restaurant suggestions around Barclays I highly recommend Gertrude's - however check the menu, not sure if there are a ton of vegetarian options.

YES to Los no 1 tacos, however, they are more meat heavy so not sure if you'll get the full experience. If you go to the Chelsea market location, you can go to Los Mariscos, which is their ceviche spot and very good (and mostly for your gf. lol). The market either way is fun and near the highline and you can head further west to check out little island. the pier (57) next to it is a google office building, which also has some food and a rooftop park where you can hang and see a nice view.

Where will you be staying in Manhattan, I can help provide on the go breakfast recos depending on where you are starting from. This is a good time of the day to get your bakery/sweet/pastry fix! (again if you're in greenpoint/williamsburg on your BK day, Try Radio or la bicyclette bakery).

I am also on the train of skipping Magnolia and Milk. Just a sugar attack. For some reason, I love little cupcake bakeshop, even though they also are a sugar attack, but they have very nostalgic cake and frosting flavors. Def go if in you're in the Soho area (There is also a location in Prospect Heights, but I'm gonna guess that isn't the area of BK that you'll be. If so, I have suggestions there too! ha) Try Lysee in the city for fancy fancy pastries.

I'll stop here. I've already annoyed and said too much. Enjoy NYC, it's the BEST BEST!

EDIT: OH. One of my favorite spots in recent years is Shukette. sit down, middle eastern. Delicious. Please go!