Wow, first time to NYC. That's a hard one, as there are so many great things to do. I agree that getting up high for a panoramic view is key. My choice: the GE building at Rockefeller Center. From there you get to see the Empire State builiding, which you don't if you go to the Empire State! Have a drink at the bar attached to the Rainbow room if you like or just have drinks there. Go at night (if they're open) for more drama.
Food would be my next focus. NY is a great food town, just skip indian, it will disappoint someone from the UK. NY reputedly has great BBQ, but I can't verify. I hear Blue Smoke is great. Asian Fusion is hot now, Buddakan (10th Av/16th St i think) is dramatically decorated, and the food's pretty good. Go across the street to Morimoto for the real deal though. For a great steakhouse in Manhattan, my vote is Keen's, on 36th off 6th Ave. Cant beat it for atmosphere - pipe collection including those owned by teddy roosevelt, buffalo bill... original program from the night Lincoln got shot upstairs. On old NY classic. Great steaks too, and a fine wine list.
Lastly, try the Staten Island Ferry. Sounds cheesy to many, it's really magical at sunset.
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