Another post for City Mapper. Just got back from a weekend in NYC and it works great - and will work in most metro areas. And subway is definitely the way to go, just pay attention to route changes/times due to track maintenance.
Yes, City Mapper is the must app for your phone. It will tell you what subways are not working etc.
Longtime resident here:
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if you want to take your car, there tends to be parking in the neighborhood around Manhattan School of Music. You would need to pay attention to the opposite-side-of-the-street parking regs. But you could do it. Commuters come in from Westchester etc in the morning on weekdays and so it can fill in the morning, but at other times it’s not so full. Weekends people are still going away for the weekend out of town and there can be on-street parking. Getting to that neighborhood, coming directly from the north is easy. You take the Taconic parkway south, to the Cross County, to the Saw Mill and then to the Henry Hudson – that takes you over a very gorgeous entrance through the north end of Manhattan. Exit on 125th street to get to Manhattan School of Music (that area looks funky but it’s where Columbia University is building its new campus – construction mess – but it’s a fine area.)
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if you decide to take the Metro North from Poughkeepsie the train goes into both the 125th street location and then to Grand Central. Getting to Manhattan School of Music from Grand Central is harder, as it’s across town from Manhattah School of Music, but Grand Central is really nice to see, and so you may just want to do that. While it’s okay to take Lyft or Via (or Uber) in town, subway is generally much faster if you need to get anywhere close to midtown, as the traffic is really crazy there.
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There are cheap places to stay in the Manhattan School of Music area and it’s not that hard to get there from 42nd street area after the show. The redline 1 train goes straight there (to either 116th or to 125th street) from Times Square, so you don’t have to change trains or anything. After the show the train is packed and there’s nothing to worry about. Cheap places to stay include the Union Theological Seminary; International House; and Teachers College Guest Rooms. These are places run by academic institutions and so they are a little more spartan than a hotel but tend to be cheaper. Union TS is like staying in a castle and it’s been used as set for many TV shows, which can be fun – https://utsnyc.edu/about/landmark/
Int. House is right on a nice quiet park – https://www.ihouse-nyc.org/guest-accommodations-nyc-housing/ -
Getting to NYU neighborhood from uptown, is not hard. The A train (subway) from 125th street is an express train and it goes directly to West 4th Street in a very short amount of time.
Use the SpotHero app to get a discounted parking spot, if you’re driving into NYC. I have a daughter at Tisch and I found a garage in the Village that charges 16.00 when I use SpotHero. Totally worth it.
Thanks, everyone! I have learned some new tricks! 
Need to load CityMapper before my next trip out.
I want to give a shout-out to the yellow taxis too! They are reliable and iconic. You can use your credit cards. Overall I trust the yellow (and uptown they are granny smith apple green) cabs any day. the drivers are tested and have ID.
I virtually always choose a yellow cab over the other ride services, if I can. FYI.
First choice: subway
Second – bus if one’s “right there” and I can hop on (use your citymapper for guidance)
Third – yellow taxi.
Thanks again everyone !!! You have all been so helpful !! Getting excited for our visit !!!
Yes, another shout out for SpotHero advanced reservations. We’ve never paid more than $25/day and you can find super low rates as well. For driving in the city, I also recommend using Waze. It gets you around the traffic and makes navigating easy. That being said, once you’re in the city and parked, the subway is the way to go most of the time.
Thanks everyone for all the help . We had no issues navigating or trip to NYC.
Spongebob was wonderful, so sad it’s closing .
My daughter enjoyed MSM and NYU. The tour guide at NYU was much better versed in MT while the guide at MSM guide didn’t know much . Both programs see like great options