Well JFK is the main airport for New York (others may be nearer to Manhatten but flights from the UK would not land there), but also consider flights to Newark as it is not much further than JFK and is about the same travelling time to Manhatten. I flew there a couple of years ago with Continental, and would rather fly with them to Newark than with BA to JFK.
Last time I went I stayed in the Pennsylvania Hotel, but even though they claimed that you had to show your room card to enter the lifts you didn't and so anyone could wander round the hotel, as evidenced by all the pizza takeaway menus etc left outside the rooms. The first time I went I stayed in the Milford Plaza hotel which is just one block from Times Square, this hotel definitely would not let anyone into the lifts unless they showed their room card, so I felt safer in this hotel than in the Penn.
http://www.milfordplaza.com/
Really, as I said before you need to invest a few hours time at your computer screen working out the best flights, hotels etc. If you're going as a family though I wonder if it would work out cheaper to rent an apartment. You could try googling 'vacation apartment new york' and see what comes up.