Manhattan

Restaurants and Cafes:

• Carbone- old-school New York Italian from the music and decor the waiter's uniforms, appetizers are prepared next to your table (prosciutto wrapped melon, caesar salad, etc.), and the vodka sauce is to die for. Fast for three days before eating here because you will certainly be rolled out (if you do it right).
• Sadelles- bagels, cream cheese, and lox perfected. For a non-sit down bagel stop that you don't need to (but still can) Instagram, hit Tompkins Square Bagels on the LES.
• BlueStone Lane- Australian coffee chain- their turmeric lattes are what dreams are made of. Their avocado toast isn't messing around either. This is the best morning/afternoon coffee staple.

Other activities:

• Top of the Rock- tourist-y of course, but still very cool experience and worth the money

Brooklyn

Restaurants and Cafes:

• Freehand Brooklyn- outdoor and indoor space, solid food and a bit scene-y, can do everything from study/get work done here to day party.

Other activities:

• North Brooklyn Farms- cool urban farm with a beautiful glass house and views of Manhattan

• DUMBO (Down Under the Manhattan Bridge Overpass)- major photo opp