Keens.
It's a steak house (pretty posh), we had an excellent chateaubriand steak, it was $90 but it was a massive portion for two. Couldn't recommend it enough.
We're off back to NYC in December and no doubt go there again.
http://www.keens.com/
Was there just last month - very impressed! Would also recommend "Ben Bensons" - beautiful steak.
I really like a place called Virgil's just off of Time Square. Also recommend a place called Katz's Delicatessen.
Would also recommend this place -
http://www.hillcountryny.com/ Really different way of serving food but great food.
Bar wise, I would recommend the Puck Fair just off of Houston and also a place called McSorleys - only go midweek though.
Tourist stuff wise, I would recommend doing the Top of the Rock during the day. I would also recommend going up either that or the Empire State buldiing at Sunset. I think that the views and general experience from the Top of the Rock far exceeds that of the Empire State building.
Would recommend doing as much walking as possible. Explore SOHO, China Town, Little Italy and those types of places on foot. Wall Street, Ground Zero and Battery Park (personal fav) are worth visiting. Walk over the Brooklyn Bridge and go to a pizza place called Grimalidi's on the Brooklyn side - don't go on a weekend as there are literally queues around the block. Check out the South City Ferry port that is close to the Brookyn Bridge. I would also suggest getting the Staten Island Ferry at around sunset, particularly on a clear night.
Time square goes without saying - again, suggest hitting it at night time if it your first time. There is a small park nearby called "Bryant Park" - also one of my fav parts of the city. Really really nice place to chill out.
Central Park is absolutely amazing and I would encourage you to spend a lot of time wandering around it. The zoo is so so but still worth a quick visit if you have time to kill. The museums are absolutely amazing by the way, especially the natural history museum. You will literally lose a day in that place.
Shopping wise, you can't go wrong with Macy's and Woodbury Common (about 50 dollar for bus from the Port Authority bus terminal). Cheap clothes is on of the pluses about any holiday to New York - both practical and fun. The price of stuff compared to the UK or Ireland is insane.
Apologies about the messy post, literally just brain dumped and am in a rush.