So since I have lived within 2 hours of NYC my whole life (right now right across the Hudson in NJ just 15 minutes away) I rarely stay in hotels, but I will tell you in Times Square the hotel no matter how luxurious will have sound issues since it is so loud there. I paid a lot to stay next to my church for my wedding and it was so loud they leave earplugs on the nightstand. Another time I stayed near Carnegie Hall and it was much quieter, don't even remember lots of late night noise. I would recommend midtown but outside Times Square. Hotels are popping up in the city like wildfire, lots of options to choose from. A lot of the new ones are fancy boutique places or Hampton Inn/Holiday Inn Express etc. For ex. there is a Hampton Inn on 31st near a restaurant we go to, the neighborhood is a bit quieter than Times Square but close to subways and if you wanted to you could hike up to the Times Square area. The key is check that your hotel if outside the tourist area is close to a few subway lines, if you are further downtown many subway lines meet in Times Square so it makes it easy to transfer on your way uptown to museums.
Learning to use the subway is really important for a good trip. Traffic is terrible and with Uber/Lyftt you have so many cars on the road you can be in a car for hours rather than the subway for 15-20 minutes to cover the same distance at rush hour. The subway is actually fairly easy to use, what will throw you off is more advanced things like construction and local vs. express. In a nutshell the lines are color coded and either a letter or number. When you are on the track you are typically going to be looking for uptown or downtown in Manhattan, but it may be classified as the borough where it is ending. I would download a map to your phone that you can access without service. Check that your stop is local or express (on the map it will be a white or black circle) so you ensure you get on a train going to your stop (many in midtown or main tourist areas are not local so it makes it a lot easier). Local goes to all stops and express skips stops. Once in a subway station if there are multiple lines just follow the signs, honestly some are a bit confusing so even New Yorkers might go down the wrong hallway on occasion if they are in an unfamiliar station. Construction is usually in the evening or weekends, however there may be delays or issues at other times so before you go underground it helps to go to MTA.info to check the status of your line on their website. There is nothing worse than swiping to find out the train is undergoing major delays due to signal issues or stopped altogether due to a sick passenger. Honestly I always say that if you are a tourist and can its best to avoid rush hour as it will be majorly stressful to get on certain lines (so crowded you may wait a few trains and then have to push your way on). New Yorkers are not as mean and scary as you might see in the movies, look for a friendly face and politely ask for help if needed. I have been on trains and 3-4 people chime in to help a tourist (New Yorkers do like to show each other how much they know about the city and how authentic they are at times so this can work to your advantage lol). Working in midtown I got stopped for directions more times than I can tell you, I have even walked tourists to the subway entrance if its only a half block out of my way and I have the time.
As for getting from airports I have used both JFK and Newark. Newark is in NJ but there is a train that goes into the city and private shuttle buses that take you into midtown for a fairly reasonable amount, so don't rule out that airport as it sometimes has lower airfare and honestly I would rather get on a shuttle bus (they are like full size coach buses by the way, not mini school buses type things) for like $15 than have to use the subway. If you choose JFK you will need a car service, taxi, or take the subway. Taxis from Newark are going to be much higher, they charge more for going across state lines. The last time we had to use JFK we took a NJ transit but to midtown from our neighborhood in NJ then got a Lyfft to JFK from port authority. This saved us at least $40 off what they were quoting us if we had them do door to door. When we got back we did the same thing. If you can book flight times not at rush hour I find it makes life much easier as the subways are less crowded if you use them and Uber/Lyfft will have lower rates if you decide to grab one of those. If you have never used those services there is often a promo for new customers and then referal promos, so for ex. you can sign up to get the discount going to the hotel, and then you can have someone else in the party sign up and get the new customer promo for the ride going back to the airport. Also don't rule out flying into one airport and then flying out of another, we have done a split like that to save money or use miles. This is one thing that is great about this city, three airports mean you can shop around
Not all subway stations are handicap accessible so if you do plan on using them with luggage (which I have done several times but honestly am not a huge fan of unless absolutely necessary) pack as light as you can since you may be carrying luggage up or down a few flights of stairs. It also helps to have a backpack as your carry on so you have to lug just the main suitcase up/down the stairs.
The streets can be a bit brutal when it comes to walking so one more tip is to pack appropriate footwear so you don't need to buy anything while there. Nice sneakers, ballet flats, and riding boots or flat booties are the way to go for major sightseeing (I recommend sneakers most of the time). I joke the city eats my shoes, I buy ballet flats on sale and am lucky if I get a year out of them before they are completely worn out even from mild use.
A good map functions (google maps or the map function on I believe booking will help show the neighborhood so you can see restaurants, shops, etc in the vicinity). 
