Looks fine overall.

Skip the Wall Street Bull, it’s a tourist trap where people line up for hours just to take a pic touching its balls. Also not much to see at City Hall, since the public isn’t allowed through the gates. You might want to keep that Lower Manhattan visit pretty short so you have lots of time to see the Frick, which is an amazing museum.

When you go to NYPL, make some time to see the Treasures exhibit, an awesome free show of the coolest objects in the library’s collection.

The Guggenheim may be skippable if you want to free up your schedule. The building is famous but it doesn’t have an especially impressive collection, though it does have great temporary shows — so check the calendar to see whether it’s showing anything that interests you.

Neue Galerie is great, you won’t regret going there.

For food, check websites like NY Eater and The Infatuation, which publish lots of guides for specific neighborhoods, cuisines, etc.

Make sure to make a reservation for the Frick in advance.

Day 3: the Cloisters are all the way uptown, not anywhere close to the Guggenheim. It’s going to be quite a day.

Also check to make sure are open the day you wanna go b

May want to stop by Christie’s (alongside Rockefeller) or Sotheby’s Breuer (near the Frick) if they’re prepping for an auction.

Also, there’s a great coffee shop, Voyager Espresso, in the Fulton St subway hallway (?) off John St, close to One WTC. They’re open weekdays.

You’re going to be really tired if this is how your days going to be. Native new Yorker. I get tired just going downtown or just walking along Central Park and walking along a lot of people. Get good walking shoes. You really going to need it

if you’re an art history student don’t limit yourself to stuffy museums which are fairly accessible yes but still cut off from view of the general nyc public. as great as they are!

walking the high line on a nice day in the morning is an important tour of the public art of this city. so is the Astor place cube) which just got reinstalled downtown near the public theater. the soldiers and sailors arch in Brooklyn just got restored too. I think that arch and grand army plaza is one of the most beautiful places in nyc.

here’s a public art map provided by city govt https://www.nycgovparks.org/art-map try to route yourself so you can walk by some of this stuff on your way to where you’re going

I truly believe NYC’s best art is not inside the museums, it’s out in the world, alive, among people walking around every day. NYC’s most prominent example of public art is, of course, the Statue of Liberty. Thanks France!

Frick is a short walk from Met and Guggenheim, you can do all 3 in one day if you have the stamina. If you’re spending 2 days on the upper east side you can include some of the art galleries located around Madison Ave in the 60’s and 70’s. As an art lover I would definitely add a half day for the Whitney, and walk from there to the Chelsea art galleries located in the west 20’s. You can also stroll around the West Village which is very lively and has great restaurants. Personally I would skip Times Square unless you’re seeing a show. If you go to the West Side you may enjoy Lincoln Center and the Folk Art Museum across the street.

I’d recommend the transit museum. It has old subway cars (that you can go inside of) and showcases the history of all of the subway, from the cars to the turnstiles. It is even inside a previous subway station.

On the north side across the street from city hall is Surrogate’s Court. It has some very interesting mosaics in the lobby. they may not let you take pictures, but they’re cool to see.

Another building with great lobby mosaics you can see for free is the ATT Long Distance building, at 32 Avenue of the Americans (once the telephone switching station for all long distances phone calls, now a generic office building)

I would not let people steer you away from Fidi. There is so much history there. It is the oldest part of Manhattan. Grab a pint or meal at Fraunces Tavern where George Washington used to drink. The Oculus is beautiful and it is amazing what they have done to rebuild. The 9/11 memorial is one of the most well done, moving memorials I have seen. You also have Trinity Church, the Battery Park City promenade with views of the Statue of Liberty. Also, you have access to Pier 11 ferry stop which is one of the best ways to see the city

• Day 3 looks ok
• Day 1 too messy and not all of these are worth it. I just don’t think FiDi is as essential as tourists treat it. But if you’re set on it you do have time for it.
• on day 4 you should just plan to be at the Met all day. It’s massive, it’s great, you’ll feel like you got your tickets worth

• on day 2 leave yourself room to stay at MoMA longer just in case. Times Square is not in itself fun unless you have something in mind. Also if you’re planning on the Morgan, go there first since it’s paid. If you then have more time you can do the other stuff

• I disagree with those saying Cloisters are too far. It’s not that bad once you’re on the subway, and you might want some time outside—fort Tryon park surrounding it is nice

Too bad ART is closed on Broadway that would’ve been perfect for you.

I feel like you're not giving yourself enough time at some of the greatest museums in the world (most of which are open for fewer than 8 hours a day) - you'll be lucky to fit everything on your list in. If you're here for the art I would come for the art and skip City Hall, the stupid bull where everyone lines up to get their photo taken with bronze testicles, and the 9/11 Memorial.
Re, timing, I would budget:
Met - entire day (you can eat lunch there)
MoMa - entire morning or afternoon (4 hours min if you want to see everything)
Guggenheim - approx 2 hours-3 hours
Frick, Morgan, Neue Gallerie - approx 2 hours each
Cloisters - 2 to 3 hours, but also takes a long time to get there and back (about an hour from midtown)
NYPL - approx 1 hour

This is how I would break up the days:

One day: Met all day (eat at museum)

Another Day: MoMa, The Cloisters. Dinner in Harlem (on the way back from the Cloisters).

Another Day: Guggenheim, Frick, Neue Gallerie (they are close by each other). Neue Gallerie has a popular cafe. Guggenheim cafe is decent and has a nice view of Central Park. Not sure about the new Frick cafe but I'm sure it's nice.

Another Day: The Morgan, NYPL, Grand Central. Grand Central has good food options in the basement (I recommend Veselka), although limited seating.

At nighttime when the museums are closed (if you aren't too tired):

One night: Walk through Central Park and end up on the Upper West side - this would be good for the day you're either at the Met or the Guggenheim, etc. The Upper West is a picturesque neighborhood to walk through, many good dinner options (use Google maps to find what you're interested in - sushi, Indian, Jewish deli, NY diner), and you could walk down through Lincoln Center which is very pretty at night, perhaps catch a performance there (eg opera) if there is anything you're interested in

Another night: Empire State Building (I'm not sure what you meant by "rooftop" but I recommend regardless). Classic art deco architecture and great views. Food Gallery 32 food court nearby in Koreatown is good for dinner or dessert

Another night: East River ferry from E 90th st or E 34th - this will take you under all of the bridges, including the Brooklyn Bridge. End at South Street Seaport and take the subway back to wherever you are staying

Another night: Walk through Times Square, walk over to Rockefeller Center and walk past Radio City Music Hall

Where are you eating all those lunch and dinners?

It’s New York, the food is the most important part

The cloisters is quite a ways away from midtown.

April in Central Park is beautiful. Hopefully there are still some tulips blooming

You're missing:

The Whitney, which is 20th century+ American Art. Also in a beautiful new building downtown with great views of the Hudson

The New Museum should be open by then. They have the most contemporary/avant garde exhibits in the City also downtown

Check the opening days of the museums that you want to visit!

The Morgan Library is closed on Mondays. The Frick is closed on Tuesdays and The Cloisters and The Met are closed on Wednesdays.

Go to the Met and the Met Cloisters the same day- your ticket into one will also get you into the other so you don’t need to pay twice. People will say you need all day for the Met- you definitely CAN spend all day (esp as you should see the full European art gallery, it’s fantastic), but I think you can spend MOST of the day there (say, 10-2) and then round it out with an hour or two at the Cloisters.

Alternatively, start your day Saturday at the Met Cloisters and then head down to the Met for the rest of the day as it’s open til 9. You really don’t need more than two hours at the Cloisters, so I’d say arrive at Ft Tryon Park between 9-10, enter the museum at 10, hang around til 12, if you feel like you need to sit down a bit take the bus from outside the door of the Met Cloisters to outside the door of the Met (it’ll take an hour plus but it is incredibly direct), otherwise take the A to the crosstown bus in under an hour, and then hang out in Central Park before arriving at the Met at 2-3 and staying til close.

Since you’re coming especially for the exhibit at the met, I would do that earlier in your trip just in case anything goes wrong - then you have some extra time to make sure you see it. The Met is also huge and if you really love art history you may decide you want to spend a second afternoon there.

I imagine you’d be bored by the cloisters as an Italian. Maybe check out Chelsea art galleries for contemporary art?