Apparently the subway is the easiest way to and from the airport. We've booked a transfer on arrival but think I'll use subway for the return trip
The easiest way from JFK to Manhattan is
Air train to Jamaica
Long Island Railroad (LIRR) to Penn
Subway from Penn
But if you’re staying in Times Square (awful awful touristy place best avoided IME) Penn is only at 34th so you can walk from there. it’s a good way to deal with the little bit of jet lag doing the transatlantic flight.
Manhattan is a very walkable city. Once you get your bearings - basically knowing whether you’re going East or West, or uptown or downtown , the best way to get a bit of the flavour of the city is to walk.
If you want bars, then the East Village is good although it’s become very gentrified in the last 10 years. I usually hang out at random bars on the Upper West Side, but that’s mainly because that’s where I’m working and living when I’m in NYC.
Non- standard touristic things are Governor's island - but sadly not in winter I thinK, unless that’s changed. worth a ferry ride in the summer, though.
Friday night at the Met - crowded but free and you can usually do a couple of galleries in the time available.
I really like the Science Museum our in Queens - built for a 1950s Expo. But if you’re only going for 4 days and you’re doing all the obvious touristic stuff, I doubt you’ll have time.
The Highline is feat, but where it finishes is still a bit of a desert for eating and drinking. I’d do it the other way ie aim to finish at the Whitney - the area around Christopher Street is lovely, although gentrified. The Village is not what it was ... but the Whitney gallery is fabulous. The Frick is wonderful too, and gives you a sense of a grand Manhattan mansion.
For glimpses of historic Manhattan, go to the Merchants House museum (East 4th I think, but then everything’s on East 4th) and/or the Tenement Museum. Really interesting insight into the development of Manhattan and also interesting areas to wander around.
The best way to get a sense of Manhattan is just to stroll its neighbourhoods. A walk up Martin Luther King Ave from say West 110th to maybe around 125th gives you a sense of Harlem, for example, and you can get a bus from there and go on to the Cloisters which is one of my favourite galleries to mooch about in.
Loads to do - just walking the streets will give you a feeling of being in a movie.
But remember the New York motto
“walk narrow or walk nimble” New Yorkers move fast and there is nothing worse than being caught behind a couple of tourists walking slowly taking up the pavement. Don’t be those people!