One of my favorite places to stay in NYC is the Renaissance Times Square. They have a lounge that overlooks Times Square that has breakfast (not free) with amazing views. Walking really is preferred in NYC. We've found it faster than taking a cab, even when going several blocks. We are sailing from there in September and will be making another trip in June to NYC before the cruise.
We fly into JFK, which always seems to be under construction. We've tried to book flights into Newark, but we live just north of Dallas and get better fares on American or SouthWest into JFK than anything into Newark. We've tried car service, cab and Uber from JFK to NYC. They recently instituted a new program that requires you to take a shuttle from the terminal to a pick up area for either a car service or an Uber/Lyft. This is intended to reduce traffic during construction, but it makes it much less convenient. The shuttles are crowded and moving your luggage on and off is a pain. It's not a long ride, but once you get to the pick up area you go to a zone and then contact your driver to tell them what zone you are in. If you take a cab into the city, you can get picked up at the curb outside the terminal. Even though the cab line is long, it's now the most convenient way to get into the city.
We love live theater so we like to go to a show (or two) when we are in town. You can choose to buy tickets in advance to the more popular shows, or you can try your luck at the TKTS window. They sell the unsold tickets to some great shows the day of the show at substantial discounts. If you have a few shows on your list that you want to see, you'll likely get some decent seats through TKTS to one you'll really enjoy.
Dining in NYC is awesome too. Really great places that offer some unique choices. I love to use YELP in NYC. You will want to make some time for a dining experience, or just choose to pick a pizza place that has good reviews if you prefer. Yelp has not done me wrong.
If you get into town with a few days to explore, consider visiting the aircraft carrier Independence. We walked there from Times Square and then back again. You could also choose to do the hop-on, hop-off bus tour. We've done this too and it's a pretty fun way to explore the island and learn a bit about it's history. Of course there are all the obvious places such as the Financial district, 9/11 memorial, Central Park and the museums.
We became somewhat familiar with the subway system as well and found it surprisingly easy to navigate. In fact, google maps set to "train" will give you all the stations, including walking directions to and from where you want to go and the stations. Super easy.
