This is madness. Are you staying in Brooklyn? Is that why you're starting and finishing your stay with sights there? Why so many parks there?
Random advice. Too many parks. While planning this, look at a map of NYC and try to schedule your visits around destinations clustered in the same area, but NYC is dense and fascinating, give yourself space/time to experience new things accidentally also.
FRIDAY Drop Hoboken. Maybe worthwhile for a much longer trip, but for a 3-day trip, unless there's a special, personal reason to head there, that's too much. Everything you want to do on Friday seems focused on downtown-ish Manhattan. So, you can combine Chinatown, Little Italy, Soho, Greenwich Village, the High Line (add this as a park, drop some of the other parks on your itinerary) on this day too. Think of Union Square (around 14th st) and Battery Park/Statue of Liberty as two end-points on your schedule for that day, and plan to do a lot of walking. Look at a map, and walk through the neighborhoods, plan a route or circuit. Almost accidentally, you're going to find yourself meandering through a variety of neighborhoods already on your list.
Side note: Manhattan's Little Italy is really small and not what it used to be. The closest thing to a real Little Italy in NYC is Arthur Avenue in the Bronx which makes a nice pairing with the nearby NY Botanical Garden also in the Bronx, but that's too far for your already packed 3-day schedule.
THURSDAY Drop Flushing Meadows Corona Park. That's really far out. Again, if you had more time, the NH which has a huge Taiwanese/Chinese presence would be interesting to check out. But the park alone is not worth a visit. Again, unless you have a compelling person reason to see the globe or the small museum there or something, cross out that park.
If you want to go to Queens, and check out probably the most concentrated place of diversity in the United States, I recommend heading to one or two of the many cool museums in western Queens.
The Museum of the Moving Image
The Noguchi Museum
PS1
But on a day where you want to do Times Square, U.N., Empire State, Central Park all that stuff, a trip out to Queens might be too much, and you might have to save it for another trip. Or you could replace one of your Brooklyn days for a mini-excursion to Queens.
The world's greatest museums are in NYC. The Metropolitan Museum of Art, MOMA (the main one - not the subsidiary PS1), Museum of Natural History, the Guggenheim, the Morgan Library & Museum, there are lots. Try one. For grandness of scale, you can't top the Metropolitan. But it gets super crowded, and if you're feeling overwhelmed/stressed, a smaller museum can feel just as exquisite but more special with more "insider" bragging rights.