Taxis don't stop for stuff. Unless you have the light, they have the right of way.
Keep train delays in mind, and when riding the subway, pay attention to the stops the train makes. Do not stop if a stranger approaches you. When using an MTA card, do not place it in your purse/pocket next to your phone; it will demagnetize.
Flushing in Queens has the best restaurants, especially L'Incontro.
Washington Heights' seediest area is between 180th and 190th, but even that area is pretty safe. There are no shootings. I would know, I go every year or so and have never observed an altercation. I assune you're talking about the musical In the Heights. That play takes place near the river in one of the safer areas of the Heights overlooking the bridge.
Go to Times Square only for tickets. Don't follow this one because I hate Times Square. If you're hetting tickets, keep in mind that the red tkts. booth is open for matinee shows and night shows at 8 and 2:30, respectivelt, I believe. Download the free app to see what stages are open. Keep in mind most stages on Broadway are dark on Mondays.
The 9/11 Memorial is serene and beautiful. It requires vistor passes for entry though. Reserve them online. The entrance is off Cordtlandt down in Battery Park.
Getting from the airport to your hotel is at your own discretion. If your hotel is in midtown, and you're coming from JFK, take the subway. If you're flying into Newark or LGA, take a taxi.
Nintendo World is worth it. Don't bother with the Empire State Building; instead, go to the Top of the Rock. The view is much nicer and you get a view of the Empire State.
My entire family is from New York and I've been tons of times. New York natives are probably a bit more help than me.
