Thank you for your answers Thereuare !
1/ Midtown: that would mean the following areas on hotwire: Central Park South, Empire State Building, Madison Square Garden, Midtown East, Rockefeller center, Time Square
2/ Agree that hotwire would be more convenient.
3/ Kids are 17, 15 and 11 years old.
4/ Budget would be indeed around $225-$250 per night per room all inclusive (taxes, fees, etc.)
5/ We would be willing to pay a bit more for extra special or convenience - I still remember my stay at the Waldorf Astoria 20 years ago 😉.
Many thanks for your help - there are so many hotels in NY!