Choose between the Empire State building and Top of the Rock. I personally prefer TOTR as you get great views of both Central Park and the ESB.
Walk over the Brooklyn bridge.
Cheesecake at Juniors in Brooklyn.
Walk the high line.
Bus tours are brilliant, as they take you to areas such as he Upper East side, Harlem etc, which are all pretty different and interesting to see.
You may well be too late to book, but look to see if there are still tickets to climb the Statur of Liberty. It’s a real climb, but amazing to do. If not, and if you like history, still do the boat tour and make time to have a good look round Ellis Island - the museum is brilliant.
If you have time, the Christmas train show at the NY botanical gardens in the Bronx is brilliant. There are amazing models of NY buildings etc, and it really is not just for train spotters
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of warm clothes. The wind chill in NY is something else, and the Christmas we were there, I found it hard to be outside without a hat, leggings under trousers and thick gloves, and I never wear these things in the UK.
In Boston, the trolley bus tours are great, and obviously the tea party ships are a must. The Mapperium (so?) is also amazing. You must also try the Cheesecake Factory. The food, both sweet and savoury is fabulous.