New York at Christmas?

I have enjoyed a couple of pre-Christmas NY trips and am now thinking about actually spending Christmas there. I have a few queries about what to expect and would appreciate any advice you could give me!
Does the city effectively 'close down' for Christmas Eve and Christmas Day or is it still possible to do shopping and enjoy the usual sightseeing activities?
Does the subway run over the holidays?
Are Restaurants very busy and if so I assume I would need to book dinner venues for 24th and 25th December?
We are planning to fly back to UK on 26th December - are flights usually quieter over the holiday period or even busier?
Also, am looking to redeem some Hilton points - any views on the Hilton Times Square and Hilton East Side?
Thanks in advance for your advice and apologies for mentioning the 'C' word so early in July!!
Turquoise
Does the city effectively 'close down' for Christmas Eve and Christmas Day or is it still possible to do shopping and enjoy the usual sightseeing activities?
Does the subway run over the holidays?
Are Restaurants very busy and if so I assume I would need to book dinner venues for 24th and 25th December?
We are planning to fly back to UK on 26th December - are flights usually quieter over the holiday period or even busier?
Also, am looking to redeem some Hilton points - any views on the Hilton Times Square and Hilton East Side?
Thanks in advance for your advice and apologies for mentioning the 'C' word so early in July!!
Turquoise